Acceleration

Very long trains can be pulled by more than one engine.

A train is made up of four engines pulling trucks filled with coal.

The coal in one truck has a mass of 75 000 kg.

gravitational field strength = 9.8 N/kg

Calculate the weight of the coal in one truck.

Use the equation:

weight = mass × gravitational field strength

One engine exerts a forward force of 850 000 N.

Calculate the work done by one engine when the train moves a distance of 80 m.

Use the equation:

work done = force × distance moved

Each of the four engines exerts a forward force of 850 000 N on the trucks.

Calculate the total forward force on the trucks.

The force exerted by the engines on the trucks is a contact force.

Which of the following is also a contact force?

Tick (✓) one box.

Which sketch graph represents the train moving at a constant speed?

Tick (✓) one box.

The train accelerates for 150 s.

The velocity of the train changes from 16 m/s to 25 m/s.

Calculate the acceleration of the train.

Use the equation:

A student investigated the acceleration of a ball dropped from different heights.

Figure 15 shows a ‘gravity ball’ that the student used.

The button on the gravity ball starts the stopwatch.

When the gravity ball hits the floor, the stopwatch stops.

This is the method used.

1. Measure a vertical height above the floor.

2. Hold the gravity ball at the measured height.

3. Start the stopwatch on the gravity ball and drop the gravity ball.

4. Record the time shown on the stopwatch.

5. Repeat steps 1 to 4 using the same height.

6. Repeat steps 1 to 5 using different heights.

The student dropped the ball from the same height five times and recorded the following results.

0.49 s 0.51 s 0.58 s 0.56 s 0.61 s

Calculate the uncertainty in these measurements of time.

What type of error caused the variation in the measurements of time?

Tick (✓) one box.

Suggest one reason for the error that caused the variation in the measurements of time.

Figure 16 shows a graph of the height the ball was dropped from against the time squared.

The acceleration of the ball can be calculated using the equation:

acceleration = 2 × (gradient of the graph)

Determine the acceleration of the ball.

A student investigated the acceleration of a ball dropped from different heights.

Figure 3 shows a ‘gravity ball’ that the student used.

The button on the gravity ball starts the stopwatch.

When the gravity ball hits the floor, the stopwatch stops.

This is the method used.

1. Measure a vertical height above the floor.

2. Hold the gravity ball at the measured height.

3. Start the stopwatch on the gravity ball and drop the gravity ball.

4. Record the time shown on the stopwatch.

5. Repeat steps 1 to 4 using the same height.

6. Repeat steps 1 to 5 using different heights.

The student dropped the ball from the same height five times and recorded the following results.

0.49 s 0.51 s 0.58 s 0.56 s 0.61 s

Calculate the uncertainty in these measurements of time.

What type of error caused the variation in the measurements of time?

Tick () one box.

Suggest one reason for the error that caused the variation in the measurements of time.

Figure 4 shows a graph of the height the ball was dropped from against the time squared.

The acceleration of the ball can be calculated using the equation:

acceleration = 2 × (gradient of the graph)

Determine the acceleration of the ball.

In a world record attempt, a skydiver jumped from a height of 40 km above the Earth.

Figure 6 shows an incomplete free-body diagram for the skydiver a few seconds after the start of the jump.

Figure 6

The skydiver has not reached terminal velocity.

Complete the free-body diagram in Figure 6.

During the first 2.5 minutes the mean acceleration of the skydiver was 0.64 m/s².

The initial velocity of the skydiver was 0 m/s.

Calculate the velocity of the skydiver 2.5 minutes after the start of the jump.

Use the Physics Equations Sheet.

The skydiver accelerated until reaching terminal velocity.

Explain why the skydiver reached terminal velocity.

Explain why the atmospheric pressure acting on the skydiver increased as the skydiver fell.

The skydiver opened his parachute.

A few seconds after opening the parachute, the resultant vertical force on the skydiver was 240 N upwards.

The wind caused a resultant horizontal force of 200 N to the left on the skydiver.

Draw a vector diagram to determine the resultant force on the skydiver.

A student investigated how changing the mass of a trolley affects the acceleration of the trolley.

Figure 5 shows some of the equipment used.

The trolley in Figure 5 is not moving.

Which force prevents the trolley from moving?

Tick (✓) one box.

The force pulling on the trolley was increased so that the trolley accelerated.

The force was then kept constant and different masses were put on the trolley.

For each different mass the acceleration of the trolley was measured.

Draw one line from each variable to the correct quantity.

For one of the masses put on the trolley, the student recorded three values of acceleration.

Calculate the mean acceleration of the trolley.

Figure 6 shows some of the results.

Describe the relationship shown in Figure 6.

When the total mass of the trolley was 1.5 kg, the acceleration of the trolley

Calculate the resultant force acting on the trolley.

Use the equation:

resultant force = mass × acceleration

A swimming pool is being filled with water.

Calculate the weight of the water in the swimming pool when the mass of the water is 25 000 kg.

gravitational field strength = 9.8 N/kg

Use the equation:

weight = mass × gravitational field strength

When the swimming pool is full, the weight of the water is 1 960 000 N.

The bottom of the swimming pool has an area of 49 m².

Calculate the pressure at the bottom of the swimming pool when it is full.

Use the equation:

Choose the unit from the box.

There is a force acting on the side of the swimming pool because of the water pressure.

Figure 11 shows the side of the swimming pool.

Which arrow shows the direction of the force acting on the side of the swimming pool?

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A child is swimming in the pool. The velocity of the child is 0.70 m/s.

The child then accelerates for 5.0 s, reaching a final velocity of 1.3 m/s.

Calculate the acceleration of the child.

Use the equation:

Figure 12 shows a diving board at the side of the swimming pool.

The original length of the spring is 0.84 m.

When the child stands on the diving board, the length of the spring decreases by 0.21 m.

Calculate the percentage change in the length of the spring.

Use the Physics Equations Sheet to answer questions 07.6 and 07.7.

Write down the equation which links extension (e), force applied to a spring (F) and spring constant (k).

The force applied to the spring by the weight of the child is 336 N.

The change in length of the spring is 0.21 m.

Calculate the spring constant of the spring.

The child steps off the diving board and falls into the swimming pool.

The initial velocity of the child is 0 m/s.

acceleration due to gravity = 9.8 m/s²

Calculate the final velocity when the child has fallen a distance of 0.95 m through the air.

Give your answer to 2 significant figures.

Use the Physics Equations Sheet.

A student investigated how the acceleration of a trolley varies with the resultant force on the trolley.

Figure 10 shows some of the equipment used.

Figure 10 shows the force F which acts through the string.

What name is given to force F ?

Give one variable that should have been a control variable in this investigation.

The student held the trolley stationary and then released it.

The trolley moved along the runway with a constant acceleration.

The student recorded the time taken for the trolley to travel a measured distance along the runway.

Describe how the acceleration of the trolley can be calculated using the time taken and distance travelled by the trolley.

For one set of results, the force acting through the string was 2.0 N.

The student released the trolley three times and determined the following values for acceleration:

Calculate the uncertainty in the values of acceleration.

The runway was then raised at one end.

The force acting through the string remained the same.

Figure 11 shows this.

Explain how the acceleration was affected by raising the end of the runway.

Figure 12 shows a velocity–time graph for a train travelling between two stations.

Determine the distance travelled by the train in the first 600 s of the journey.

Explain what happens to the braking force as the train decelerates.

Use information from Figure 12.

Determine the maximum deceleration of the train.

Another train travels at a speed of 60 m/s.

A constant braking force of 270 000 N causes the train to decelerate and stop.

mass of train = 240 000 kg

Calculate the distance travelled while the braking force is applied.

Use the Physics Equations Sheet.

It is illegal for train drivers to drink alcohol before driving a train.

Explain how drinking alcohol would affect the stopping distance of a train.

Figure 25 shows the route an aeroplane takes as it travels from an airport terminal to the runway. Figure 25 has been drawn to scale.

Determine the magnitude of the aeroplane’s displacement from the start point to the finish point on Figure 25.

Figure 26 shows the direction of the horizontal forces acting on the aeroplane as it moves in a straight line towards the runway.

Determine the magnitude of the resultant horizontal force on the aeroplane.

Describe the motion of the aeroplane as it moves towards the runway.

Air resistance and friction are contact forces. Give one other example of a contact force.

The aeroplane stops for a short time and then accelerates along the runway. Figure 27 shows a distance–time sketch-graph for this stage of the journey.

Draw the velocity–time sketch-graph for this stage of the journey on Figure 28.

The aeroplane takes off from the runway, so its height above the ground increases. Figure 29 shows how atmospheric pressure varies with the height of the aeroplane above the ground.

Estimate the atmospheric pressure when the height of the aeroplane above the ground is 10 km.

What happens to the air surrounding the aeroplane as the height of the aeroplane above the ground increases? Tick (✓) one box.

Some cars have a lever that is used to apply the handbrake. Figure 8 shows the handbrake lever in a car.

The driver applies the force shown in Figure 8. The force produces a moment about the pivot. How could the driver increase the moment about the pivot without increasing the size of the force?

The driver releases the handbrake. Figure 9 shows how the velocity of the car changes during the first 5 seconds of a journey.

After 3 seconds, the momentum of the car is 24 000 kg m/s. Calculate the mass of the car. Use the Physics Equations Sheet.

Determine the distance travelled by the car during the first 5 seconds of the journey. Use Figure 9.

In an emergency the driver needs to apply the brakes suddenly to stop the car quickly. The driver of the car is distracted. Explain why the distraction will increase the stopping distance.

Explain why the temperature of the brakes increases as they are used.

Figure 14 shows some bumper cars. Bumper cars are designed to withstand collisions at low speeds.

During a collision between a bumper car and the barrier, the bumper car and barrier act as a closed system. What is meant by a ‘closed system’?

How does Newton’s Third Law of motion apply to the collision between the bumper car and the barrier?

During the collision, the change in momentum of the bumper car is 700 kg m/s. The time taken for the collision is 0.28 s. Calculate the force on the bumper car during the collision. Use the Physics Equations Sheet.

The bumper car has a flexible bumper. Explain how the flexible bumper reduces the risk of injury to the people in the bumper car during the collision.

A bumper car moved with an initial constant velocity and then accelerated

While accelerating, the bumper car travelled a distance of 1.5 m. The final velocity of the bumper car was 2.5 m/s. Calculate the initial constant velocity of the bumper car. Use the Physics Equations Sheet.

Hailstones are small balls of ice. Hailstones form in clouds and fall to the ground.

Figure 3 shows different-sized hailstones.

Which force causes the hailstones to fall to the ground?

Tick (✓) one box.

As the hailstones begin to fall they accelerate.

Which force increases as the hailstones accelerate?

Tick (✓) one box.

After a short time hailstones fall at terminal velocity.

Which of the following statements is true at terminal velocity?

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A scientist investigated how the terminal velocity of hailstones varies with their diameter.

Figure 4 shows the results.

Estimate the terminal velocity for a hailstone with a diameter of 80 mm.

Show how you obtain your answer.

Give one reason why a hailstone with a large diameter has a greater terminal velocity than a hailstone with a smaller diameter.

Tick (✓) one box.

After falling, the hailstone hits the ground.

Figure 5 shows the forces acting on the hailstone at the moment it hits the ground.

What is the magnitude of the resultant force on the hailstone in Figure 5 ?

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What is the direction of the resultant force on the hailstone in Figure 5 ?

Figure 15 shows an electric super-car.

The battery in an electric car needs to be recharged.

Suggest two factors that affect the distance an electric car can travel before the battery needs to be recharged.

Use the Physics Equations Sheet to answer questions 08.2 and 08.3.

Write down the equation which links acceleration (a), change in velocity (Δ v) and time taken (t).

The maximum acceleration of the car is 20 m/s².

Calculate the time taken for the speed of the car to change from 0 m/s to 28 m/s at its maximum acceleration.

In a trial run, the car accelerates at 10 m/s² until it reaches its final velocity.

distance travelled by the car = 605 m

initial velocity of the car = 0 m/s

Calculate the final velocity of the car.

Use the Physics Equations Sheet.

Use the Physics Equations Sheet to answer questions 08.5 and 08.6.

Write down the equation which links distance (s), force (F) and work done (W).

When travelling at its maximum speed the air resistance acting on the car is 4000 N.

Calculate the work done against air resistance when the car travels a distance of 7.5 km at its maximum speed.

Figure 1 shows an electric super-car.

The battery in an electric car needs to be recharged.

Suggest two factors that affect the distance an electric car can travel before the battery needs to be recharged.

Use the Physics Equations Sheet to answer questions 01.2 and 01.3.

Write down the equation which links acceleration (a), change in velocity (Δ v) and time taken (t).

The maximum acceleration of the car is 20 m/s².

Calculate the time taken for the speed of the car to change from 0 m/s to 28 m/s at its maximum acceleration.

In a trial run, the car accelerates at 10 m/s² until it reaches its final velocity.

distance travelled by the car = 605 m

initial velocity of the car = 0 m/s

Calculate the final velocity of the car.

Use the Physics Equations Sheet.

Use the Physics Equations Sheet to answer questions 01.5 and 01.6.

Write down the equation which links distance (s), force (F) and work done (W).

When travelling at its maximum speed the air resistance acting on the car is 4000 N.

Calculate the work done against air resistance when the car travels a distance of 7.5 km at its maximum speed.

Hailstones are small balls of ice. Hailstones form in clouds and fall to the ground.

Figure 7 shows different-sized hailstones.

A hailstone falls from a cloud and accelerates.

Why does the hailstone accelerate?

The hailstone stops accelerating and reaches terminal velocity.

Explain why the hailstone reaches terminal velocity.

A scientist investigated how the mass of hailstones affects their terminal velocity.

Figure 8 shows the results.

Why does terminal velocity increase with mass?

Tick (✓) one box.

Explain the difference in the maximum kinetic energy of a hailstone with a mass of 10 g and a hailstone with a mass of 20 g.

The kinetic energy of a hailstone is measured in joules.

Which of the following is the same as 1 joule?

Tick (✓) one box.

Figure 8 is repeated below.

A hailstone hit the ground at its terminal velocity of 25 m/s.

The hailstone took 0.060 s to stop moving.

Determine the average force on the hailstone as it hit the ground.

Use information from Figure 8.

Use the Physics Equations Sheet.

Figure 3 shows a cyclist on a bicycle. The cyclist is moving at a constant velocity. Arrows A and B represent the horizontal forces acting on the bicycle and cyclist.

What is force A ? Tick (✓) one box.

What is force B ? Tick (✓) one box.

What is the relationship between force A and force B when the cyclist travels at a constant velocity? Tick (✓) one box.

The cyclist applies a force of 150 N to one of the bicycle pedals. Figure 4 shows the distance between the force applied and the pivot.

Calculate the moment about the pivot caused by the force applied to the pedal in Figure 4. Use the equation: moment of a force = force × distance

Figure 5 shows how the pedal is connected to the back wheel of the bicycle.

Complete the sentence. Choose the answer from the box.

axle chain cog

The force from the cyclist pushing down on the pedal is transmitted to the back wheel

Figure 6 shows how the velocity of the cyclist changes during a journey.

What is the change in velocity of the cyclist in the first 20 seconds of the journey? Tick (✓) one box.

Determine the acceleration of the cyclist during the first 20 seconds of the journey. Use your answer from Question 02.6 Use the equation:

Complete the sentence. Choose the answer from the box.

deceleration speed velocity

Between 30 and 40 seconds the cyclist moves with

The cyclist travels from home to school. Figure 7 shows the route the cyclist followed.

Draw an arrow on Figure 7 to show the displacement of the cyclist.

Figure 11 shows a cyclist riding a bicycle. Force A causes the bicycle to accelerate forwards.

What name is given to force A ?

Figure 12 shows how the velocity of the cyclist changes during a short journey.

Determine the distance travelled by the cyclist between Y and Z.

Figure 13 shows the gears on the bicycle.

Describe how the force on the pedal causes a moment about the rear axle.

Figure 14 shows a different cyclist towing a trailer.

The speed of the cyclist and trailer increased uniformly from 0 m/s to 2.4 m/s. The cyclist travelled 0.018 km while accelerating. Calculate the initial acceleration of the cyclist.

The resultant force of the towbar on the trailer has a horizontal component and a vertical component. horizontal force = 200 N vertical force = 75 N

Determine the magnitude and direction of the resultant force of the towbar on the trailer by drawing a vector diagram.

An aircraft travels at a constant velocity. How is the velocity of the aircraft different to the speed of the aircraft?

Figure 11 shows one of the engines on the aircraft.

Air is taken into the front of the engine and pushed out of the back of the engine. Explain the effect this has on the engine.

Figure 12 shows a distance-time graph for the aircraft.

Determine the speed of the aircraft.

Write down the equation that links acceleration (a), change in velocity (Δ v) and time taken (t).

At a different stage of the flight, the aircraft was travelling at a velocity of 250 m/s. The aircraft then decelerated at 0.14 m/s². Calculate the time taken for the aircraft to decelerate from 250 m/s to 68 m/s.

Write down the equation that links distance (s), force (F) and work done (W).

When the aircraft landed, it travelled 2000 m before stopping. The work done to stop the aircraft was 140 000 000 J. Calculate the mean force used to stop the aircraft.

Mean force = N

Figure 8 shows a student playing with a remote-controlled car.

The remote control transmits radio waves to the car aerial. The transmitted radio waves have a frequency of 320 MHz. speed of radio waves = 3.0 10⁸ m/s Calculate the wavelength of the radio waves. Give the unit.

The car aerial is connected to an electrical circuit in the car. Describe what happens in the electrical circuit when the car aerial absorbs radio waves.

The car produces sound waves. Give two ways in which radio waves are different to sound waves.

Figure 9 shows the distance-time graph for the first 30 seconds of the car’s motion.

Describe the motion of the car during the first 30 seconds.

Determine the speed of the car 20 seconds after it started to move.

A different car accelerated from 0.12 m/s to 0.52 m/s. The acceleration of the car was 0.040 m/s². The work done to accelerate the car was 0.48 J. Calculate the resultant force needed to accelerate the car.

Explain why the car has a maximum speed.

The following statements describe parts of a short train journey between two railway stations. Part A: The train accelerates at a constant rate from 0 m/s to 20 m/s in 40 s Part B: The train travels at a constant velocity for 260 s Part C: The train decelerates at a constant rate coming to a stop in 60 s

During which part of the journey is the resultant force on the train zero? Tick (✓) one box.

Figure 16 shows part of the velocity-time graph for the train journey. Complete Figure 16 showing part B and part C of the train journey.

Figure 16

Write down the equation which links acceleration, change in velocity and time taken.

Another train accelerated at 1.15 m/s² for 22.0 s Calculate the increase in velocity of the train.

An aeroplane is 4000 m above the Earth’s surface. A skydiver jumps from the aeroplane and falls vertically. Figure 15 shows the distance the skydiver falls during the first 12 seconds after jumping.

Figure 16 shows part of the free body diagram for the skydiver three seconds after jumping. Complete the free body diagram for the skydiver.

Explain the changing motion of the skydiver in terms of the forces acting on the skydiver.

Use Figure 15 to determine the speed of the skydiver between 7 seconds and 12 seconds.

In 2012 a skydiver jumped from a helium balloon 39 000 metres above the Earth’s surface. The skydiver reached a maximum speed of 377 m/s Jumping from 39 000 metres allowed the skydiver to reach a much higher speed than a skydiver jumping from 4000 metres. Explain why.

A child drops a ball. The ball hits the ground and bounces. Figure 14 shows the velocity-time graph for the ball from when the ball is dropped until when the ball reaches the top of its first bounce. Air resistance has been ignored.

Figure 14

Describe the motion of the ball between points A and B on Figure 14.

What direction is the ball moving between points C and D on Figure 14 ?

The ball and the Earth form a system. What is meant by ‘a system’? Tick one box.

When the ball hits the ground, energy is transferred from the ball to the Earth. Explain how the data in Figure 14 shows this energy transfer.

A child drops a ball. The ball hits the ground and bounces. Figure 1 shows the velocity-time graph for the ball from when the ball is dropped until when the ball reaches the top of its first bounce. Air resistance has been ignored.

Describe the motion of the ball between points A and B on Figure 1.

What direction is the ball moving between points C and D on Figure 1 ?

The ball and the Earth form a system. What is meant by ‘a system’? Tick one box.

When the ball hits the ground, energy is transferred from the ball to the Earth. Explain how the data in Figure 1 shows this energy transfer.