Acceleration

Figure 5 shows a velocity / time graph for a car moving on a test track.

Use this graph to describe the velocity of the car in stages TS, SR and RQ.

TS

SR

RQ

State how the motion of the car is different in RQ compared with QP.

Calculate the acceleration of the car in Figure 5 in the first 5 s.

Use the equation

acceleration =_........ m / s²

Calculate the distance travelled by the car in Figure 5 from 5 s to 15 s.

Figure 10 shows a skier sliding down a slope.

The gravitational potential energy of the skier decreases by 39 000 J between the top and the bottom of the slope.

The mass of the skier is 70 kg.

Calculate the height, h of the slope.

The value of g is 10 N / kg.

Use the equation

Δ GPE = m × g × h

The skier starts from rest at the top of the slope.

The velocity of the skier at the bottom of the slope is 27 m / s.

Using information from Figure 10, calculate the acceleration of the skier along the slope.

acceleration =_........ m / s²

When the skier slides from the top to the bottom of the slope, some energy is dissipated.

Explain how to determine the amount of energy dissipated.

Figure 11 shows athletes running at a constant speed on a curved section of

Even though they are running at a constant speed, the velocity of each athlete is changing.

State why the velocity of each athlete is changing.

The athletes start the race on a straight section of track.

Figure 12 shows a distance / time graph for one of the athletes.

Determine the gradient of this graph at a time of 2.5 s.

gradient =_........

A car is being driven at a constant velocity.

The driver sees an obstacle in the road ahead.

The driver uses the brakes to stop as quickly as possible.

Figure 9 shows the velocity/time graph for the car from the time when the driver sees the obstacle.

Which of these is the driver’s reaction time shown in Figure 9?

State one factor that might increase a driver’s reaction time.

Calculate the distance travelled between when the driver applies the brakes and when the car comes to rest in Figure 9.

Use the equation

distance = area under the sloping line of the graph in Figure 9

The stopping distance of a car is the thinking distance plus the braking distance.

A car has a device that can detect an obstacle in the road ahead.

The device is linked to a computer that can apply the brakes.

It is claimed that, in an emergency, the computer-controlled car will have a shorter stopping distance than if the car is controlled by a human driver.

Explain why this claim could be true.

A different car has a device that can detect rain.

This device is linked to a computer that can change the speed of the car.

In wet weather, the computer changes the speed of the car.

State the change in speed that the computer should make when the road is wet.

Give a reason why this change in speed is necessary when the road is wet.

Two people, L and M, have a 100 m race.

L starts running before M.

Figure 20 shows a distance/time graph of the race.

State the distance that L has run when M overtakes.

Calculate the velocity of L when running the 100 m race.

A motorcycle is travelling at a velocity of 6.2 m/s.

The motorcycle accelerates at 2.5 m/s² until its velocity is 10 m/s.

Calculate the time taken for this acceleration.

Use the equation

The motorcycle now decelerates (slows down) from 10 m/s to a stop.

The deceleration is at a constant rate of 4.4 m/s².

Calculate the distance the motorcycle travels as it slows down to a stop.

Use the equation

*(c) A student has a trolley and a ramp, as shown in Figure 21.

The height, H, of one end of the ramp can be adjusted.

The student investigates how the average speed of the trolley between X and Y depends on the height, H, of the ramp.

Describe

• the additional equipment that the student needs

• how that equipment is used to obtain the measurements needed.

Two people, L and M, have a 100 m race.

L starts running before M.

Figure 4 shows a distance/time graph of the race.

State the distance that L has run when M overtakes.

Calculate the velocity of L when running the 100 m race.

A motorcycle is travelling at a velocity of 6.2 m/s.

The motorcycle accelerates at 2.5 m/s² until its velocity is 10 m/s.

Calculate the time taken for this acceleration.

Use the equation

The motor cycle now decelerates (slows down) from 10 m/s to a stop.

The deceleration is at a constant rate of 4.4 m/s².

Calculate the distance the motorcycle travels as it slows down to a stop.

Use the equation

A car collides with a barrier on a road.

The time of the collision is very short.

Explain one factor, other than the time of the collision, that would affect the force on the car in the collision.

Your explanation should refer to an equation in the Equation Booklet.

A car starts from rest and then travels for 70 s as shown on the graph in Figure 11.

Complete the sentence using data from Figure 11.

The car is travelling at constant velocity from_........ s

Use data from the graph in Figure 11 to show that the car travels a total distance of about 710 m in 70 s.

Calculate the average speed of the car for the total distance travelled.

The inertial mass of an object is a measure of how difficult it is to change the velocity of the object.

A force of 450 N acts on a car to give the car an acceleration of 0.35 m/s².

Calculate the inertial mass of the car.

inertial mass of car_........

Figure 12 shows a different velocity/time graph.

This straight line graph can be represented by the equation

Give the quantities that x and y represent in the equation.

Calculate the value of m from the graph in Figure 12.

State the value of c from the graph in Figure 12.

The graph in Figure 5 shows how the velocity of a car changes with time.

The car starts from rest and travels along a level, straight road for 50 s.

Which part of the graph shows when the car has constant velocity?

Which part of the graph shows when the car has the greatest acceleration?

Calculate the acceleration of the car in the first 10 s shown on the graph.

Use the equation

acceleration =_........ m / s

Calculate the distance the car travels in part QR shown on the velocity / time graph in Figure 5.

A different car has a mass of 1200 kg.

Calculate the force needed to give this car an acceleration of 2.4 m / s².

Use the equation

F = m × a

Which of these is a scalar quantity?

A student has some cupcake cases.

One cupcake case is shown in Figure 14.

The student drops a stack of cupcake cases with the base facing downwards, as shown in Figure 15.

(Source: © Elena Schweitzer/Shutterstock)

Figure 15

The speed of the falling stack of cupcake cases depends on the number of cupcake cases in the stack.

The student also has a stop clock and a metre rule.

Describe an investigation to show how the speed of the falling stack of cupcake cases depends on the number of cupcake cases in the stack.

A stack of cupcake cases has a mass of 0.005 kg.

Calculate the weight, in newtons, of the stack of cupcake cases.

Gravitational field strength = 10 N / kg

Use the equation

W = mg

Figure 16 shows a cupcake case that is falling at a constant velocity.

Draw an arrow on Figure 16 to show the force due to air resistance on the cupcake case.

State the value of the acceleration of the cupcake case when it is falling at a constant velocity

A car travels along a straight road.

The car accelerates at 3 m / s² for a time of 7 s.

Calculate the change in velocity of the car.

Use the equation

change in velocity = acceleration × time taken

Figure 5 shows a football kicked against a wall.

The football has a mass of 0.42 kg.

The football gains 11 J of gravitational potential energy as it moves from the ground to the wall.

Calculate the height at which the ball hits the wall.

Gravitational field strength = 10 N / kg

Use the equation

∆ GPE = m × g × ∆ h

Calculate the kinetic energy of the football when it is moving at a velocity of 12 m / s.

Use the equation

Describe the energy transfers that happen when the ball hits the wall.

A stone is held at rest above the ground.

The stone is released and falls until its velocity is 17 m / s.

Calculate the distance the stone has fallen when its velocity has reached 17 m / s.

Figure 8 is a velocity/time graph for a lift moving upwards in a tall building.

For what length of time is the lift at rest during the first 16 s?

Use the graph in Figure 8 to determine the maximum velocity of the lift during the first 16 s.

Use the graph in Figure 8 to determine the acceleration of the lift during the first 1.4 s.

acceleration =_........ m / s²

Use the graph in Figure 8 to determine the distance that the lift travelled during the first 6.0 s.

At 18 s, the lift starts to move downwards.

Sketch a line on the graph in Figure 8 to show the lift moving downwards after 18 s.

Figure 15 is a speed limit sign from a European motorway.

The speeds shown are in km/h (kilometres per hour).

The sign tells drivers to drive at a slower speed in wet weather.

Explain why it is safer for drivers to drive at a slower speed in wet weather.

Show that a speed of 31 m/s is less than a speed of 130 km/h.

A car is travelling at a speed of 31 m/s.

The car travels 46 m between the driver seeing an emergency and starting to brake.

Calculate the driver’s reaction time.

Give your answer to 2 significant figures.

driver’s reaction time =_........

*(b) Figure 16 is a velocity/time graph for a toy train on a straight track for 7 seconds.

Using information from the graph, describe when and how the velocity and acceleration of the toy train change at different times during the 7 seconds shown on the graph.

An aircraft starts from rest and accelerates along the runway for 36 s to reach take‑off velocity.

Take‑off velocity for this aircraft is 82 m/s.

Show that the acceleration of the aircraft along the runway is about 2 m/s².

Assume the acceleration is constant.

Calculate the distance the aircraft travels along the runway before take‑off.

Use the equation

Suggest one reason why the length of the runway used is always much longer than the calculated distance that the aircraft travels along the runway before take-off.

The aircraft lands with a velocity of 71 m/s.

Calculate the kinetic energy of the aircraft as it lands.

When the aircraft has come to a stop, all the kinetic energy has been transferred to the surroundings.

Give one way that the energy has been transferred to the surroundings.

A car is travelling at 10 m/s.

The driver sees a danger and stops the car.

The stopping distance for the car would be smaller if the car

Figure 4 shows a speed-time graph for the driver stopping the car.

Use the graph to find the driver’s reaction time.

Figure 5 shows the apparatus a student uses to investigate how the stopping distance of a toy car depends on the type of surface that it is stopping on.

toy car

Describe an experiment to find out how the stopping distance depends on the surface that stops the toy car.

Figure 6 shows a set of results used to find the average stopping distance of the toy car on a surface.

State the anomalous value of stopping distance given in the table in Figure 6.

Use the results in Figure 6 to calculate the average stopping distance.

State one way the student could increase the speed of the car as it reaches the flat surface.

A car is travelling down a slope at 2.0 m/s.

The car accelerates for 4.0 s.

The speed of the car increases to 12 m/s.

Calculate the acceleration of the car.

Use the equation

acceleration of the car =_........ ²

Quantities can be either scalar or vector.

Which of these is a vector quantity?

Figure 7 shows a ball bearing as it falls slowly through a clear, dense liquid.

The apparatus in Figure 7 is used to find the average speed of the ball bearing as it falls.

Devise an experiment to determine the average speed of the ball bearing as it falls through the liquid.

You should include:

• any extra apparatus you would use to take measurements

• the measurements you would take

• how you would calculate the speed.

A student thinks that the ball bearing falls through the liquid at a constant speed.

Explain how you could develop this experiment to determine if the ball bearing falls through the liquid at constant speed.

You may draw a diagram to help your answer.

The ball bearing is now dropped through air.

The initial velocity of the ball bearing is zero.

The acceleration of the ball bearing is 10m/s².

The ball bearing falls 1.5 m.

Calculate the velocity of the ball bearing when it has fallen 1.5 m.

Use the equation

Figure 8 is a velocity/time graph showing a 34 s part of a train’s journey.

Calculate the acceleration of the train in the 34 s.

Give your answer to an appropriate number of significant figures.

acceleration =_........ ²

Calculate the distance the train travels in the 34 s.

Figure 9 shows a rocket soon after it takes off from the ground.

The force that the rocket engines produce remains constant during the first few seconds after take-off.

Explain what happens to the acceleration during the first few seconds.

Figure 10 shows a small steel ball held at a height, h, above the ground.

The ball is released and allowed to fall to the ground.

The height h is 1.4 m.

Calculate the time, t, for the ball to reach the ground.

Use the equation

Two students use the arrangement shown in Figure 10.

They use a stopwatch to time the ball falling through the height of 1.4 m.

The students repeat the measurement many times, but their average value for t is different from the calculated value.

Suggest a reason why the students’ value for t is different from the calculated value.

Suggest one improvement the students could make to their procedure so that their value for t is closer to the calculated value.

Figure 11a shows a box falling towards a hard floor.

The box hits the floor and crumples a little before it comes to rest as shown in Figure 11b.

The momentum of the box just before it hits the floor is 8.7 kg m/s.

The box comes to rest 0.35 s after it first hits the floor.

Calculate the magnitude of the force exerted by the floor on the box.

Use an equation selected from the list of equations at the end of this paper.

State the magnitude and direction of the force exerted by the box on the floor.

Figure 12 shows a ball held in a clamp at R, above the ground.

The ball is released from the clamp and falls.

S is 3.8 m below R.

At S the momentum of the ball is 0.40 kg m/s.

Calculate the mass of the ball.

Acceleration due to gravity, g, = 10 m / s²

mass of the ball_........

Which of these is a vector?

State the equation that relates acceleration to change in velocity and time taken.

A van accelerates from a velocity of 2 m / s to a velocity of 20 m / s in 12 s.

Calculate the acceleration of the van.

acceleration =_........ m / s²

Figure 17 is a velocity / time graph for 15 s of a cyclist’s journey.

Calculate the distance the cyclist travels in the 15 s.

*(d) Many factors can affect the stopping distance of a car.

Some of these factors involve the driver and some of these factors involve the car or the road.

Explain how the stopping distance of a car is affected by

• factors involving the driver

• factors involving the car or the road.

You should include examples in your explanations.

Which of these is a vector?

State the equation that relates acceleration to change in velocity and time taken.

A van accelerates from a velocity of 2 m / s to a velocity of 20 m / s in 12 s.

Calculate the acceleration of the van.

acceleration =_........ m / s²

Figure 3 is a velocity / time graph for 15 s of a cyclist’s journey.

Calculate the distance the cyclist travels in the 15 s.

Another cyclist starts from rest, but his acceleration decreases as time increases.

Sketch the velocity / time graph for this cyclist on Figure 3.

The force that keeps an object moving in a circular path is known as the

Figure 11 shows an object moving in a circular path.

Draw an arrow on Figure 11 to show the direction of the force that keeps the object moving in a circular path.

The object in Figure 11 is moving at constant speed.

Explain why it is not moving with constant velocity.

Figure 12 shows a skier on a slope.

The skier travels down the slope with a constant acceleration.

The speed of the skier is measured at points P and Q.

The table in Figure 13 gives some data about the skier making one downhill run.

Calculate the distance from P to Q.

Use an equation selected from the list of equations at the end of this paper.

Calculate the time taken for the skier to travel from P to Q.

The symbol ‘ g ’ can be used to refer to the acceleration due to gravity.

The acceleration due to gravity ‘g’ has the unit of m/s².

‘ g ’ can also have another unit.

Which of these is also a unit for g ?

Two students try to determine a value for g, the acceleration due to gravity.

They measure the time, t, for a small steel ball to fall through a height, h, from rest.

They measure t to be 0.74 s, using a stopwatch.

They measure h to be 2.50 m, using a metre rule.

Calculate a value for g from the students’ measurements.

Use the equation

They record the time t for two more drops from the same height.

The three values for time t are

0.74 s, 0.69 s, 0.81 s.

Calculate the average value of time t to an appropriate number of significant figures.

Explain one way the students could improve their procedure to obtain a more accurate value for g.

A car travelling at 15 m/s comes to rest in a distance of 14 m when the brakes are applied.

Calculate the deceleration of the car. Use an equation selected from the list of equations at the end of this paper.