Kinematics

Define velocity.

Determine the time taken for the ball to reach the wall.

$\text{time taken}$ = ______ $\text{s}$

Calculate the vertical component $u$ of the initial velocity of the ball.

$u$ = ______ $\text{m s}^{-1}$

The ball just goes over the wall.

Calculate the height $h$ of the wall.

$h$ = ______ $\text{m}$

Define acceleration.

On Fig. 1.1, draw a line to show the path of the parcel as it falls from the aircraft to the ground.

Calculate the time taken from the instant of release to the instant the parcel reaches the ground.

time = ______ $\text{s}$

Calculate the vertical component of the velocity of the parcel immediately before it reaches the ground.

vertical component of velocity = ______ $\text{m s}^{-1}$

Determine the speed at which the parcel reaches the ground.

speed = ______ $\text{m s}^{-1}$

State what is represented by the area under a velocity–time graph.

the acceleration of trolley B during the collision

acceleration of B = ______ $\text{m s}^{-2}$

the magnitude and direction of the final velocity of trolley A.

magnitude = ______ $\text{m s}^{-1}$
direction ______

On Fig. 3.2, sketch the variation of the velocity of trolley A with time $t$ from $t = 0$ to $t = 0.50\ \text{s}$.

Show that the ball reaches a maximum height above the ground of $4.7\ \text{m}$.

The man does not catch the ball as it falls.

Calculate the time taken for the ball to fall from its maximum height to the ground.

time taken = ______ $\text{s}$

The ball leaves the man’s hand at time $t = 0$ and hits the ground at time $t = T$.

On Fig. 3.2, sketch a graph to show the variation of the velocity $v$ of the ball with time $t$ from $t = 0$ to $t = T$. Numerical values of $v$ and $t$ are not required. Assume that $v$ is positive in the upward direction.

State what is represented by the gradient of the graph in (c).

the magnitudes of their accelerations

the speeds with which they hit the ground.

Define acceleration.

Explain why the force due to air resistance acting on the ball may be neglected when calculating the time taken for the ball to reach the beam of light.

Calculate the time taken for the ball to fall from rest to position P where the bottom of the ball touches the beam of light.

time taken = ______ $\text{s}$

Determine the time interval during which the beam of light is broken by the ball.

time interval = ______ $\text{s}$

A different ball is released from the same position as the steel ball in (b). This ball has the same diameter but a much lower density. For this ball, the force due to air resistance cannot be neglected as the ball falls.

State and explain the change, if any, to the time interval during which the beam of light is broken by the ball.

The speed limit for cars on the road is $100\ \text{km h}^{-1}$. State and explain whether car Q exceeds the speed limit.

Calculate the acceleration of car P.

acceleration = ______ $\text{m s}^{-2}$

Determine the distance between the two cars at time $t = 12\ \text{s}$.

distance = ______ $\text{m}$

From time $t = 12\ \text{s}$, the velocity of each car remains constant at its value at $t = 12\ \text{s}$.

Determine the time $t$ at which car Q passes car P.

$t$ = ______ $\text{s}$

Define speed and velocity and use these definitions to explain why one of these quantities is a scalar and the other is a vector.

speed: ......................................................................................................................................

velocity: .....................................................................................................................................

The variation with time $t$ of the velocity $v$ of the ball is shown in Fig. 2.2.

Air resistance is negligible.

Without calculation, use Fig. 2.2 to describe the variation with time $t$ of the velocity of the ball from $t = 0$ to $t = 2.1\ \text{s}$.

Calculate the acceleration of the ball after it rebounds from the ground. Show your working.

acceleration = ______ $\text{m s}^{-2}$

Calculate, for the ball, from $t = 0$ to $t = 2.1\ \text{s}$,

1. the distance moved,

distance = ______ $\text{m}$

1. the displacement from the initial position.

displacement = ______ $\text{m}$

On Fig. 2.3, sketch the variation with $t$ of the speed of the ball.

Use Fig. 2.1 to describe, without calculation, the speed of the stone from $t = 0$ to $t = 3.0 \text{ s}$.

the speed at $3.0 \text{ s}$,

speed = ______ $\text{m s}^{-1}$

the distance travelled from $t = 0$ to $t = 3.0 \text{ s}$,

distance = ______ $\text{m}$

the displacement from $t = 0$ to $t = 3.0 \text{ s}$.

displacement = ______ $\text{m}$
direction ______

On Fig. 2.2, draw the variation with time $t$ of the velocity $v$ of the stone from $t = 0$ to $t = 3.0 \text{ s}$.

Define velocity.

Distinguish between speed and velocity.

calculate the distance moved by the car,

distance = ______ $\text{m}$

calculate the magnitude of the resultant force on the car.

resultant force = ______ $\text{N}$

The direction of motion of the car in (b) at time $t = 2.0\ \text{s}$ is shown in Fig. 1.2.

On Fig. 1.2, show with arrows the directions of the acceleration (label this arrow A) and the resultant force (label this arrow F).

Complete Fig. 2.2 for the time until the ball reaches B.

Calculate the maximum height reached by the ball.

$\text{height}$ = ______ $\text{m}$

Calculate the horizontal component $V_h$ of the velocity of the ball at time $t = 0$.

$V_h$ = ______ $\text{m s}^{-1}$

On Fig. 2.2, sketch the variation with $t$ of $V_h$. Label this sketch $V_h$.

the maximum kinetic energy,

$\text{maximum kinetic energy}$ = ______ $\text{J}$

the maximum potential energy above the ground.

$\text{maximum potential energy}$ = ______ $\text{J}$