Kinematics I

Graph

The graph of velocity against time for an object moving in a straight line is shown.

Which of the following is the corresponding graph of displacement against time?

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A ball is released from rest above a horizontal surface. The graph shows the variation with time of its velocity.

Areas X and Y are equal.

This is because

• the ball’s acceleration is the same during its upward and downward motion.

• the speed at which the ball leaves the surface after an impact is equal to the speed at which it returns to the surface for the next impact.

• for one impact, the speed at which the ball hits the surface equals the speed at which it leaves the surface.

• the ball rises and falls through the same distance between impacts.

A car at rest in a traffic queue moves forward in a straight line and then comes to rest again. The graph shows the variation with time of its displacement.

What is its speed while it is moving?

• 0.70 m s^-1

• 0.80 m s^-1

• 1.25 m s^-1

• 1.40 m s^-1

A car is travelling with uniform acceleration along a straight road. The road has marker posts every 100 m. When the car passes one post, it has a speed of 10 m s^–1 and, when it passes the next one, its speed is 20 m s^–1.

What is the car’s acceleration?

• 0.67 m s^-2

• 1.5 m s^-2

• 2.5 m s^-2

• 6.0 m s^-2

When a car driver sees a hazard ahead, she applies the brakes as soon as she can and brings the car to rest. The graph shows how the speed v of the car varies with time t after the hazard is seen.

Which graph represents the variation with time t of the distance s travelled by the car after the hazard has been seen?

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An object falls 10.0 m from rest before entering some water.

Assuming negligible air resistance, what is the time taken to reach the water and the speed with which the object reaches the water?

• A

• B

• C

• D

The diagram shows a velocity-time graph for a car.

What is the distance travelled between time t = 0 and t = 4 s?

• 2.5 m

• 3.0 m

• 20 m

• 28 m

A football is dropped from a building.

Which acceleration-time graph best represents the motion of the football through the air (air resistance is assumed negligible)?

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Two markers M1 and M2 are set up a vertical distance h apart.

A steel ball is released at time zero from a point a distance x above M1. The ball reaches M1 at time t1 and reaches M2 at time t2. The acceleration of the ball is constant.

Which expression gives the acceleration of the ball?

• $\frac{2h}{t_2^2}$

• $\frac{2h}{\left(t_2+t_1\right)}$

• $\frac{2h}{\left(t_2-t_1\right)^2}$

• $\frac{2h}{\left(t_2^2-t_1^2\right)}$

The diagram shows a velocity-time graph for a mass moving up and down on the end of a spring.

Which point represents the velocity of the mass when at the lowest point of its motion?

• A

• B

• C

• D