From conservation of energy, the distance the spring should be compressed is 2 cm
What is Work ?The work done on an object is the product of force and distance in the direction of the force.
Given that a student attempts to fire a small steel sphere (mass = 250 g) into a cup from a spring-loaded cannon affixed to a table.
The cup is located 74.7 cm from the table's edge.
If compressing the spring by 2.2 cm results in the sphere travelling 82.2 cm, then,
the elastic potential energy = work done on the object
1/2ke² = Fs
Where F = mg = 0.25 × 9.8
F = 2.45 N
1/2 × k × (2.2/100)² = 2.45 × 82.2/100
0.000242K = 2.0139
k = 2.0139/0.000242
k = 8321.9 N/m
The distance the spring should be compressed in order to project the sphere into the cup can be known by using the same formula since k is the same elastic constant.
1/2ke² = Fs
1/2 × 8321.9 × (e)² = 2.45 × 74.7/100
4161e² = 1.83015
e² = 1.83015/4161
e² = 0.00044
e = √0.00044
e = 0.02 m
e = 2 cm
Therefore, the spring should be compressed by 2 cm in order to project the sphere into the cup.
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what does air resistance do when an object falls
Answer:slows it down
Explanation:when something drops it slow down
Answer: increase
Explanation: Air resistance is increases with velocity. When object fall , the velocity will increase. so, resistance will increase.
A 15 g toy car moving to the right at 22 cm/s
has a head-on nearly elastic collision with a
22 g toy car moving in the opposite direction
at 31 cm/s. After colliding, the 15g car moves
with a velocity of 42 cm/s to the left.
Find the speed of the second car after the
collision.
Answer in units of cm/s. Answer in units
of cm/s.
Answer:
Explanation:
The speed of the second car after the collision can be found using the law of conservation of momentum. The law states that the total momentum of a system remains constant if no external forces act on it.The initial momentum of the first car is (15g)(22 cm/s) = 330 g cm/s to the right.
The initial momentum of the second car is (22g)(-31 cm/s) = -682 g cm/s to the left.
The total initial momentum of the system is 330 g cm/s - 682 g cm/s = -352 g cm/sAfter the collision, the final momentum of the first car is (15g)(-42 cm/s) = -630 g cm/s to the left.
The final momentum of the second car is (m)(v) where m is the mass of the second car and v is the speed after the collision.
The total final momentum of the system is -630 g cm/s + (m)(v) = -352 g cm/s (since it remains constant)Therefore, m*v = -630 g cm/s + 352 g cm/s = -278 g cm/sTo find v, we need to divide the momentum by the mass
v = -278 g cm/s / 22 g = -12.6 cm/sSo the speed of the second car after the collision is -12.6 cm/s to the left.
If I have a BEYBLADE spinning for about 34 seconds, how many mph does it spin? If I have a BEYBLADE that spins for 42 seconds, how many mph does it spin?
34 second beyblade speed= 1 rotation every 00.1 second
42 second beyblade speed= 1 rotation every 0.00001 second
These are estimated speeds. I think this because the speed of the beyblade.
the information provided (34 and 42 seconds) does not give the necessary information to determine the speed at which the BEYBLADE is spinning in miles per hour. To calculate the speed of the BEYBLADE we need to know the distance traveled in each rotation. Also, you mentioned that the beyblade makes 1 rotation in 34 seconds and 42 seconds, which is not correct, it should be 1 rotation per second in 34 seconds, and 1 rotation per 42 seconds.
A 5kg drone is moving through the air. If the drone has 40 J of kinetic energy, how fast is the drone moving?
____m/s
Answer:
4 m/
Explanation:
Kinetic energy = 1/2 mv²
40 = 1/2 × 5 × v²
v² = (40 × 2) ÷ 5
v = sqrt(16) [square root]
v = 4
Two forces are acting on the ring in figure. What is the magnitude and direction of the net force acting on the ring?
a) the net force is acting on the figure as shown is 896 N
b) The direction of this net force that is acting on the object is 44.4°
What is the net force?We know that force is a vector quantity. As such, we have that singular force that would have the same effect in magnitude and direction as the two forces acting together. We are to obtain the magnitude of this force and its direction.
We can tell that;
Vertical component = 500 sin 40 = 321.4 N
400 sin 50 = 306.4 N
= 627.8 N
Horizontal Component = 500 cos 40 = 383 N
400 cos 50 = 257 N
= 640 N
The resultant now is;
R = √(627)^2 + (640)^2
R = 896 N
The direction is; Tan-1 (627.8/640) = 44.4°
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The following equation estimates the average calories burned for a person when exercising, which is based on a scientific journal article (source):
Calories = ( (Age x 0.2757) + (Weight x 0.03295) + (Heart Rate x 1.0781) — 75.4991 ) x Time / 8.368
Write a program using inputs age (years), weight (pounds), heart rate (beats per minute), and time (minutes), respectively. Output the average calories burned for a person.
Output each floating-point value with two digits after the decimal point, which can be achieved as follows:
print('Calories: {:.2f} calories'.format(calories))
Ex: If the input is:
Here is an example of a Python program that calculates the average calories burned for a person based on the equation provided:.
def calories_burned(age, weight, heart_rate, time):
calories = ((age * 0.2757) + (weight * 0.03295) + (heart_rate * 1.0781) - 75.4991) * time / 8.368
return calories
age = int(input("Enter your age in years: "))
weight = int(input("Enter your weight in pounds: "))
heart_rate = int(input("Enter your heart rate in beats per minute: "))
time = int(input("Enter the duration of your exercise in minutes: "))
print("You have burned an average of", calories_burned(age, weight, heart_rate, time), "calories.")
What is the program about?This program defines a function calories_burned() that takes four inputs: age, weight, heart rate, and time. The function then uses the provided equation to calculate the average calories burned and returns the result.
The program also prompts the user to enter their age, weight, heart rate, and time, and then prints the result of the calculation.
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Which civilization was the first to use zero as a placeholder?
O Romans
O Greek
O Chinese
O Hindus of India
Explanation:
It might seem like an obvious piece of any numerical system, but the zero is a surprisingly recent development in human history. In fact, this ubiquitous symbol for “nothing” didn’t even find its way to Europe until as late as the 12th century. Zero’s origins most likely date back to the “fertile crescent” of ancient Mesopotamia. Sumerian scribes used spaces to denote absences in number columns as early as 4,000 years ago, but the first recorded use of a zero-like symbol dates to sometime around the third century B.C. in ancient Babylon. The Babylonians employed a number system based around values of 60, and they developed a specific sign—two small wedges—to differentiate between magnitudes in the same way that modern decimal-based systems use zeros to distinguish between tenths, hundreds, and thousandths. A similar type of symbol cropped up independently in the Americas sometime around 350 A.D., when the Mayans began using a zero marker in their calendars.
These early counting systems only saw the zero as a placeholder—not a number with its own unique value or properties. A full grasp of zero’s importance would not arrive until the seventh century A.D. in India. There, the mathematician Brahmagupta and others used small dots under numbers to show a zero placeholder, but they also viewed the zero as having a null value, called “sunya.” Brahmagupta was also the first to show that subtracting a number from itself results in zero. From India, the zero made its way to China and back to the Middle East, where it was taken up by the mathematician Mohammed ibn Musa al Khwarizmi around 773. It was al-Khowarizmi who first synthesized Indian arithmetic and showed how the zero could function in algebraic equations, and by the ninth century, the zero had entered the Arabic numeral system in a form resembling the oval shape we use today.
The zero continued to migrate for another few centuries before finally reaching Europe sometime around the 1100s. Thinkers like the Italian mathematician Fibonacci helped introduce zero to the mainstream, and it later figured prominently in the work of Rene Descartes along with Sir Isaac Newton and Gottfried Leibniz’s invention of calculus. Since then, the concept of “nothing” has continued to play a role in the development of everything from physics and economics to engineering and computing.
Hope it Helps and PLEASE DO NOT FORGET TO RATE-ME DOWN BELOW!Eve's
contractor recommended she not install baseboard heating. In which scenario would it be disadvantageous to install a baseboard heating system?
A. Where there is high room air circulation
B. Where there are low ceiling heights
C. Where electricity is generated from a gas-fired plant
D. Where the TD is zero
Mark for review (Will be highlighted on the review page)
Installing an underfloor heating system in a situation where the electricity is generated by a gas-fired plant would not be advantageous.
What is electricity exactly?Charge or electrical supply flow is what is referred to as electricity. It is an alternative fuel source, which means we obtain it by transforming other natural resources into energy supplies, such as carbon, dirty energy, hydrocarbons, and nuclear energy.
How does electricity get made?To create electricity, a turbine set converts mechanical energy into electrical energy. The heat produced by sources of energy such natural gas, carbon, nuclear reactors, biomass, petroleum, volcanic, and solar heat is employed to transform to steam, which powers the rotors of turbines.
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3 A uniform plank of weight 120N rests on two stools as
shown in Fig. 5.16. A weight of 80N is placed on the
plank, midway between the stools. Calculate:
a the force acting on the stool at A,
b the force acting on the stool at B.
I’m confused on how to calculate moment of weight if there are two pivots
The force acting on the stools of the 88N and 112N.
What is meant by force?
An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.The application of force is the location at which force is applied, and the direction in which the force is applied is known as the direction of the force.The word "force" has a specific meaning in science.At this level, calling a force a push or a pull is entirely appropriate.A force is not something an object "has in it" or that it "contains." One thing experiences a force from another.There are both living things and non-living objects in the concept of a force.A uniform plank of weight 120N rests on two stools as a midway between the stool.
(80 × 1.25) + (120 × 1.5) = B × 2.5
B = 112N
80 × 1.25) + (120 × 1.0) = A × 2.5
A = 88N
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.
A hot rod of mass 1200 kg, starting from rest
reaches a speed of 110 m/s in only 18.3 s.
What is the average output power?
The average output power of the hot rod is 793,442.62 W.
What is the average output power?
The average output power is calculated by applying the following equation for average power.
P = Fv
where;
F is the average force applied by the objectv is the velocity of the objectBut force, F = ma
where;
a is the acceleration of the objectm is the mass of the objectP = ( ma ) x ( v )
P = ( m x v/t ) x ( v )
P = ( mv² ) / ( t )
where;
t is the time of motion
The average output power of the hot rod is calculated as follows
P = ( 1200 x 110² ) / ( 18.3 )
P = 793,442.62 W
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the period of a simple pendulum increases by 50% when the length of the pendulum is increased by 0.6 m.
The intial length of the pendulum is
a) 1.2m
b) 0.48m
c) 0.24m
d) 0.12m.
Answer:
b) 0.48m is the right answer.
a ball is projected with initial velocity 40m/s at angle of 27° from a building 60meters high.find total time the ball is in the air
Answer:
projectile motion
total time of flight= 2V° Sintheta / g
answer is 3second
Hope This would help you!
Alexa exerts a force of 560 N on the
ground, due to her weight.
a) When Alexa is wearing high-heeled
shoes, the total area of her shoes in
2
contact with the ground is 58 cm².
When she has bare feet, the total area of
her feet in contact with the ground is
230 cm².
2
Calculate the difference between the
pressure she exerts on the ground when
she is wearing these shoes and when she
has bare feet.
Give your answer in N/cm² to 1 d.p.
Answer:
[tex]\Delta P \approx 7.2 \ N/cm^2}[/tex]
Explanation:
To calculate the difference in pressure that Alexa exerts on the ground when wearing high-heeled shoes compared to when she has bare feet, we can use the following formula for pressure:
[tex]\rightarrow P=\dfrac{F}{A}[/tex]
Where:
"F" is the force exerted in the ground."A" is the area the force is applied to.First, let's calculate the pressure when Alexa is wearing high-heeled shoes:
F = 560 N (given)
A = 58 cm² (given)
[tex]P_h=\dfrac{560}{58}\\\\\\\\\therefore P_h \approx 9.655 \ N/cm^2[/tex]
Next, let's calculate the pressure when Alexa has bare feet:
F = 560 N (given)
A = 230 cm² (given)
[tex]P_b=\dfrac{560}{230}\\\\\\\\\therefore P_h \approx 2.435 \ N/cm^2[/tex]
Finally, let's calculate the difference in pressure:
[tex]\Delta P= P_h-P_b\\\\\\\\\Longrightarrow \Delta P =9.655-2.435\\\\\\\\\therefore \boxed{\boxed{\Delta P \approx 7.2 \ N/cm^2}}[/tex]
Therefore, the difference in pressure that Alexa exerts on the ground when wearing high-heeled shoes compared to when she has bare feet is approximately 7.2 N/cm².
It’s 2:00pm. The local weather station is tracking a violent storm that is traveling east at 25 km/hr. It is 75km west of Ft. Collins. Daniel starts riding his bike home at 5:00. Will he be home before the storm hits?
To determine whether Daniel will be home before the storm hits, we need to determine the time it will take for the storm to reach Fort Collins and compare it to the time it will take for Daniel to reach home by bike.
Given:
Storm's speed = 25 km/hr = 25000 m/hr
Distance from Fort Collins = 75 km = 75000 m
Time of storm = distance / speed = 75000 m / 25000 m/hr = 3 hrs
If Daniel starts riding his bike home at 5:00pm, he needs to cover the distance from where he is to his home before the storm hits Fort Collins.
If he is able to maintain an average speed of 20km/h = 20000 m/h,
time = distance/speed = 75000 m/20000 m/h = 3.75 hrs
Since the storm will take 3 hours to reach Fort Collins and Daniel will take 3.75 hours to reach home by bike, he will be home before the storm hits.
At which location would a bowling ball have the greatest weight? on Earth, at the top of a tall mountain on the surface of the moon on Earth, several kilometers below the surface on Earth at sea level
Several Kilometres below the earth at Sea level
.
An 1750 kg car is coasting along a level road at 30 m/s. A constant braking force is applied, such that the car is stopped in a distance of 60 meters. What is the magnitude of the braking force?
The magnitude of the constant braking force applied on the car is 13125 Newton.
What is force?The definition of force in physics is: The push or pull on a massed object changes its velocity. An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.
A spring balance can be used to calculate the Force. The Newton is the SI unit of force.
The magnitude of the braking force is = 1750 kg × (30)² ÷ (2 × 60) Newton
= 13125 Newton.
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A runner whose initial speed is 29 km/h increases her speed to 31 km/h in
order to win a race. If the runner takes 5.0 seconds to complete this
increase in her speed, what is her acceleration?
I need this answered asap!!!
The acceleration of the runner is 0.12 m/s^2.
What is the acceleration?We have to note that the term acceleration would have to do with the rate of the change of the velocity of the object with time. Now we have to note that in this case, we would have to change the velocities of the body to the unit of meter per second.
Initial velocity = 29 km/h or 8 m/s
Final velocity = 31 km/h or 8.6 m/s
We then have that;
a = v - u/t
Then we can be able to substitute the values and have;
a = 8.6 - 8/5
= 0.12 m/s^2
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An observer in a truck observes a billboard appearing to move -21m/s to the east (east being in the +x direction), while a skater appears to be skating 24.94m/s 38 degrees north of west (north being in the +y direction, west in the −x direction). What is the velocity of the skater relative to the billboard?
The velocity of the skater relative to the billboard is 5.65 m/s east.
What is the velocity of the skater relative to the billboard?
The velocity of the skater relative to the billboard is the measure of the change in position of the skater with respect to the billboard. That is, how fast is the skater moving away from the billboard.
Considering the signs of east and west direction, the formula for the relative velocity of the Skater is given as;
Vs/B = Vs - VB
where;
Vs is the velocity of the skater with respect to the observerVB is the velocity of the billboard with respect to the observerThe magnitude of the velocity of the skater in west direction is given as;
Vs = V cos ( θ )
where;
V is the magnitude of the velocityθ is the angle of velocity of the skater with respect to x axisVs = 24.94 m/s x cos ( 90 - 38 )
Vs = 24.94 m/s x cos ( 52 )
Vs = 15.35 m/s
The velocity of the skater relative to the billboard is calculated as follows;
west = negative direction
east = positive direction
Vs/B = -15.35 m/s - ( -21 m/s )
Vs/B = 5.65 m/s
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A student solving a physics problem to find the unknown has applied physics principles and obtained the expression: μkmgcosθ=mgsinθ−ma , where g=9.80meter/second2 , a=3.60meter/second2 , θ=27.0∘ , and m is not given. Which of the following represents a simplified expression for μk ?
The simplified expression for the coefficient of kinetic friction is 0.097.
What is the coefficient of kinetic friction?The coefficient of kinetic friction is described as the ratio of the kinetic friction force of contacting surfaces to the normal force.
The simplified expression for the coefficient of kinetic friction is calculated as follows;
μkmgcosθ = mgsinθ − ma
m(μkgcosθ) = m(gsinθ − a)
μkgcosθ = gsinθ − a
μk= gsinθ − a/ gcosθ
where;
μk is the coefficient of kinetic friction g is the acceleration due to gravityθ is the anglea is the acceleration of the objectWe have the given parameters:
g = 9.8 m/s²
a = 3.6 m/s²
θ=27.0∘
μk = (9.8 sin 27.0 ) - 3.6 / 9.8 cos27.0
μk = 0.097
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The space shuttle Copernicus is docking with an orbiting space station for refueling. Copernicus has a mass of 20,000 kg and approaches the station with a speed of 50 m/s . The space station has a mass of 80,000 kg and is floating toward the space ship with a speed of 10 m/s . How fast will Copernicus and the space station be moving after they have successfully docked? *Hint* remember that the direction of speed matters.
Copernicus and the space station will be moving at 2 m/s after they have successfully docked.
What is law of conservation of momentum?According to the law of conservation of momentum, absent an external force, the combined momentum of two or more bodies operating upon one another in an isolated system remains constant.
From law of conservation of momentum, we can write:
Total initial momentum = Total final momentum
80000 kg × (- 10 m/s) + 20000 kg × (+ 50 m/s) = (80000 kg + 20000 kg) × (v m/s)
v = 2 m/s.
Hence, Copernicus and the space station will be moving at 2 m/s after they have successfully docked.
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A SpaceX Crew Dragon with a mass of 5,000 kg is approaching the International Space Station (ISS). The mass of the ISS is 420,000 kg. The table below shows the magnitude of the gravitational forces each object exerts on each other at various ranges:
Range Force on Crew Dragon Force on ISS
1 km 1.4 E−7 N 5.4 E−8 N
500 m 5.6 E−7 N 1.3 E−6 N
200 m 3.5 E−6 N 3.5 E−6 N
100 m 1.4 E−5 N 1.4 E−7 N
Which of the following table entries is correct for their interaction?
A. 1 km
B. 500 m
C. 200 m
D. 100 m
C. 200 m
The gravitational force between two objects is determined by the mass of each object and the distance between them. The gravitational force is inversely proportional to the square of the distance between the objects and directly proportional to the product of the masses. The gravitational force exerted by the ISS on the Crew Dragon is equal in magnitude but opposite in direction to the force exerted by the Crew Dragon on the ISS.
In the table provided, at a range of 200 m, the force on the Crew Dragon is 3.5 E-6 N and the force on the ISS is 3.5 E-6 N, showing that the forces are equal and opposite in direction. At other ranges, the force on the Crew Dragon and the force on the ISS are not equal, this means that the gravitational force at 200m is correct for their interaction.
How much power does it take to lift 30.0 kg 10.0 m high in 5 seconds
Answer:
About 600 watts
Explanation:
Work = force x distance = 30 x 10 x 10 = 3000 J. Power = Work done/time = 3000/ 5 = 600 watts.
Three forces are acting on the ring as shown in the figure. What is the magnitude and direction of the net force acting on the ring?
Answer:
The magnitude and direction of the net force acting on the ring is equal to the vector sum of the three forces acting on it. Based on the figure, the net force acting on the ring is equal to the vector sum of F1 minus F2 plus F3, and its magnitude is equal to the square root of (F1^2 + F3^2) minus (F2^2). The direction of the net force is the same as that of F1 minus F2 plus F3. This is because the three forces, F1, F2, and F3, all act concurrently and will add up to produce a single resultant, or net force.
The driver of a car traveling at 31.3 m/s applies the brakes and undergoes a constant
deceleration of 1.6 m/s^2.
How many revolutions does each tire make
before the car comes to a stop, assuming that
the car does not skid and that the tires have
radii of 0.31 m?
Answer in units of rev.
The distance the car travels before coming to a stop can be calculated using the equation d = (v^2 - u^2)/2a, where v is the initial velocity, u is the final velocity, and a is the acceleration.
What is acceleration?
Acceleration is the rate of change of velocity over time. It is defined as the rate at which an object's speed or direction changes with respect to time. Acceleration is a vector quantity, meaning it has both magnitude and direction.
The SI unit for acceleration is meters per second squared (m/s2). It is also commonly expressed in feet per second squared (ft/s2). Acceleration can be positive, negative, or zero. Positive acceleration occurs when an object increases its speed, and negative acceleration when it decreases its speed. Zero acceleration occurs when an object's speed remains constant.
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Two objects are accelerated equal amounts, but one object takes less force. Explain how and list a real life example of this scenario.
Answer:
A real-life example of this scenario can be seen in the operation of a car. When a car is accelerating, the engine applies a force to the wheels, which in turn apply a force to the ground. The car and its contents (including passengers) have a certain mass, and the force applied by the engine must be sufficient to accelerate this mass to a higher velocity. However, if the car is carrying a heavy load, such as a trailer, the total mass of the car and the load is greater, so it will take more force to accelerate the combined mass to the same velocity as a car without a load.
Explanation:
Two objects can be accelerated by the same amount but with different forces if they have different masses. This is because force is equal to mass times acceleration (F = ma), so if the mass of one object is greater than the other, it will take more force to accelerate it by the same amount.
Another example could be a person trying to push a boulder and a beach ball. The person will apply the same force but the boulder will move less distance than the beach ball.
A rigid disk, of homogeneous material, mass equal to 1 kg and radius 50 cm, is kept spinning on the floor without friction around an axis with constant angular velocity. A small ball, much smaller in size than the disk and with a mass equal to one-twentieth of the disk, is initially at a radial distance from the center of the disk equal to half the radius. After 10 s the ball arrives at the end of the disk and exits.
1. To what forces is the ball subjected in the reference system integral with the floor?
2. To what forces is the ball subjected in the reference system integral with the disk and having its
origin at the center of it?
3. What kind of motion does the ball have in both of the above reference systems?
4. Calculate the rotational velocity of the disc.
5. How, if at all, would the motion of the disk vary once the ball leaves it,
assuming it is no longer kept in constant rotation? (Type of motion and angular velocity
angular)?
Un disco rigido, di materiale omogeneo, massa pari a 1 Kg e raggio 50 cm, è mantenuto in rotazione sul pavimento senza attrito attorno ad un asse con velocità angolare costante. Una pallina, di dimensioni molto più piccole del disco e massa pari a un ventesimo del disco, si trova inizialmente ad una distanza radiale dal centro del disco pari alla metà del raggio. Dopo 10 s la pallina arriva all'estremità del disco e ne fuoriesce. 1. A quali forze è soggetta la pallina nel sistema di riferimento solidale con il pavimento?
2. A quali forze è soggetta la pallina nel sistema di riferimento solidale con il disco e avente origine al centro dello stesso?
3. Che tipo di moto ha la pallina in entrambi i sopracitati sistemi di riferimento?
4. Calcolare la velocità di rotazione del disco.
5. Come varierebbe, se varierebbe il moto del disco una volta che la pallina lo abbandona, nell'ipotesi che non sia più mantenuto in rotazione costante? (Tipo di moto e velocità angolare)?
Answer:
In the reference system integral with the floor, the ball is subjected to the force of gravity pulling it downwards towards the floor and a normal force pushing it upwards to balance the force of gravity. The ball is also subjected to the centrifugal force pushing it outwards away from the center of the disk.
In the reference system integral with the disk and having its origin at the center of it, the ball is not subjected to any net force. The centrifugal force is balanced by a centripetal force pulling it towards the center of the disk.
In both reference systems, the ball has a combination of circular motion and linear motion. In the reference system integral with the floor, the ball is moving in a circular path due to the centrifugal force and is also moving away from the center of the disk. In the reference system integral with the disk, the ball is moving in a circular path with a constant speed.
To calculate the rotational velocity of the disc, we can use the formula v = r * w, where v is the rotational velocity, r is the radius of the disk and w is the angular velocity. Therefore, the rotational velocity of the disk is v = 0.5 m * w = 25m/s
Once the ball leaves the disk, the disk will no longer be balanced and will lose angular momentum, so it will slow down and eventually stop spinning. The motion of the disk will change from rotational motion to translational motion. The angular velocity of the disk will decrease to zero.
8. The time it takes a rock thrown straight up at 10 m/s to return to its starting position is about.
Answer: 2.04 Seconds
Explanation:Use t=(2v)/g = (2)(10)/9.8 = 2.04 seconds
the distance covered by a car at a time t is given by x=20t+6t^4. calculate the instantaneous velocity and acceleration when t= 1s.
Answer:
t = 1s is 44 m/s and 72 m/s^2
Explanation:
The distance covered by a car at a time t is given by x=20t+6t^4. To calculate the instantaneous velocity and acceleration when t=1s, we can use the formulas for velocity and acceleration, which are:
Velocity (v) = dx/dt = d/dt(20t+6t^4) = 20 + 24t^3
Acceleration (a) = dv/dt = d/dt(20 + 24t^3) = 72t^2
When t = 1s, we can substitute this value into the formulas for velocity and acceleration:
Velocity (v) = 20 + 24(1)^3 = 20 + 24 = 44 m/s
Acceleration (a) = 72(1)^2 = 72 m/s^2
Therefore, the instantaneous velocity and acceleration of the car when t = 1s is 44 m/s and 72 m/s^2, respectively.
Macmillan Learning
Steve races to the nearest taco stand at lunchtime and sees that his pedometer recorded his peak speed at 72.3 cm/s. What was
Steve's peak speed in kilometers per hour?
peak speed=
km/h
Need help with the conversion set up!!
The Steve’s peak speed after conversion from centimeter per second to kilometer per hour would be 2.6 km/h
The rate of change in distance over a certain period of time is the definition of speed. It has a distance by time dimension. You may calculate speed by multiplying the SI unit of length, which is meters, by the SI unit of time, which is seconds (seconds).
Multiplying a speed measurement in centimeters per second by the appropriate conversion ratio enables one to convert that speed measurement to kilometers per hour. You can convert using this simple method, which takes into account the fact that one centimeter per second is equivalent to 0.036 kilometers per hour:
kilometers per hour = centimeters per second × 0.036
= 72.3 × 0.036
=2.6 km/h
To learn more about conversion, click here:
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The equal and opposite forces described by Newton's third law of motion will balance each other out in many cases.
True
False
