Equations of Motion (CIE A Level Physics)

Define acceleration.

A ball is kicked from horizontal ground towards a vertical wall, as shown in Fig. 1.1.

Fig. 1.1 (not to scale)

The horizontal distance between the initial position of the ball and the base of the wall is 24 m. The ball is kicked with an initial velocity v at an angle of 28° to the horizontal. The ball hits the top of the wall after a time of 1.5 s. Air resistance is negligible.

v_x = ................................................. m s^–1 [1]

[2]

time = ....................................................... s [2]

Fig. 1.2

[2]

maximum height = ...................................................... m  [2]

mass = ..................................................... kg  [2]

A ball of greater mass is kicked with the same velocity as the ball in (b).

Air resistance is still negligible. 

State and explain the effect, if any, of the increased mass on the time taken by the ball to reach its maximum height.

A boy standing on a cliff shoots a pellet from his pellet gun vertically upwards. The variation of displacement s of the pellet with time t is shown in Fig. 1.1.

[2]

On Fig. 1.2, sketch the variation of velocity v of the pellet with time t.

Include your values from (a) on the axes.

Using Fig. 1.2

An identical pellet gun is fired horizontally off the edge of the cliff at the exact same time the other gun is fired vertically upwards. The vertically fired pellet is in motion for exactly 6.0 s before hitting the ground below the edge of the cliff.

Both pellets have the same initial speed.

A ball is projected horizontally at 27 m s^–1 from a vertical cliff. It travels a horizontal distance of 40 m before hitting the ground.

Assume that air resistance is negligible.

Calculate the vertical velocity of the ball just before it hits the ground.

Calculate the height of the cliff.

Sketch the graphs to show how the horizontal and vertical components of the velocity of the ball,  and  change with time t just before the ball hits the ground.

Label any appropriate values on the axes.

Calculate the resultant velocity of the ball just before it hits the ground.

A particle moves in a straight line with a constant acceleration, a. The initial velocity of the particle at t = 0 is u.  After a further time t, its velocity has increased to v.

A student investigates the motion of a light ball bearing as it falls from rest alongside a vertical 100 cm scale.

The student sets up a camera to take flash photographs of the ball at 0.05 s intervals, as shown in Fig. 1.1.

The first photograph is taken at time t = 0.

Using Fig. 1.1, describe and explain the motion of the ball

The 100 cm scale is suspended 160 cm above the ground.

Determine the total time that the ball spends in free fall after it is dropped from the starting point of the 100 cm scale.

The student repeats the experiment with a lead sphere that falls with constant acceleration and does not reach a constant speed.

Determine the number of photographs, including the photograph at t = 0, that will be observed against the 100 cm scale.

An archer fires an arrow towards a target as shown in Fig. 1.1.

The centre of the target is at the same height as the initial position of the arrow.

The target is a distance of 100 m from the arrow. The arrow has an initial velocity of 62 m s^–1 and is fired at an angle of 11° to the horizontal.

Describe how the vertical and horizontal components of the arrow's velocity change from when it is fired until it reaches its maximum height. 

Assume that the effect of air resistance is negligible.

Show that the time taken for the arrow to reach its maximum height is about 1.2 s.

Calculate the horizontal distance, measured along the base line, by which the arrow misses the target.

A motorcyclist practices a stunt on a ramp inclined such that they leave it at an angle of 25º and 3 m high as shown in Fig. 1.1.

The other ramp is 24 m away and has a height of 1 m, as shown.

Fig. 1.1

Calculate the minimum initial velocity the motorcyclist requires in order to reach the other ramp.

The stunt motorcyclist's ultimate goal is to jump across a river and land on the other side. Fig. 1.3 shows the motorcyclist driving off a ramp at the edge of a river.

Fig. 1.3

The ramp is at an angle of 25° to the horizontal and the height at the end of the ramp is 3.0 m. The width of the river is 100 m. The initial velocity of the motorcyclist is 35 m s⁻¹.

Deduce whether the motorcyclist lands on the other side of the river.

Explain how air resistance would affect the jump.

An object is released near the surface of the Moon at time t = 0. Fig. 1.1 shows the variation of displacement s with time t of the object from the point of release. 

Fig. 1.1

Use the graph in Fig. 1.1 to determine a value for the acceleration of free fall close to the surface of the Moon.

Use Fig. 1.1 to estimate the instantaneous velocity of the object when t = 1.5 s.

A rock is thrown horizontally off a 175 m high cliff and lands 105 m away. 

Calculate the resultant velocity at which it hits the ground, assuming air resistance is negligible. 

The rock hits the ground at an angle θ  to the horizontal.

Determine, without calculation, how the angle will change if the stone is thrown in the same way with a greater velocity. 

The rock is now attached to a catapult and launched at a castle wall. The rock is launched at an angle of 30º from the horizontal at a speed of 29 m s^–1. The castle wall is 50 m away and is 15 m high. 

Determine whether the rock makes it over the wall.

sin(2A) = 2sin(A)cos(A) is a double angled formula. 

Justify that, in the absence of air resistance, the maximum range of any projectile that starts and ends at ground level is achieved when it is launched at 45^o to the horizontal. 

A bus driver drives with a constant acceleration of 5.0 m s^–2 from an initial velocity of 3.0 m s^–1. After 2.5 seconds, they slow down to stop at a set of traffic lights at 4.0 m s^–2, eventually coming to a complete stop.  Assume that air resistance is negligible.

Calculate the distance between where the bus began to accelerate and the traffic lights where the bus stops. 

On Fig. 1.1 draw the velocity­–time graph for the motion of the bus. 

Fig. 1.1