4.3 Equations of Motion

A girl jogs at in a straight line at an angle of 37^o to north for 30 seconds. Her initial velocity is 1.0 m s^–1.

She accelerates at a contant rate and covers a displacement of 125 m in the direction of travel.

What is her acceleration in an easterly direction?

A stunt motorcyclist attempts to jump a stream of width, w, which is equal to 0.15n × value of h, where n is an integer value. The bank from which the motorcyclist takes off has height, h, above the level of the water in the stream. The opposite bank has a height of 0.3h. 

The time of flight of the motorcyclist is 6 s, and they only just make the opposite bank.

Which of the following cannot be a value of W?

An astronaut standing on the surface of the Earth is able to throw a ball directly upwards to a height of 3.4 m.

When he travels to the moon, he throws the same ball at an angle of 28^o off a cliff of height 10 m with the same initial velocity. The ball strikes the ground at a point of distance d from the base of the cliff.

Assume no air resistance on the Earth or Moon. The acceleration due to gravity on the moon compared to the Earth is 0.17g.

What is the value of d?

A car travels along a horizontal road starting at time t = 0. It finishes its journey at t = . At time t the car has travelled a distance of x = R sin (4t).

The speed of the car at time t is given by v = 4R cos (4t). The acceleration is given by a = -16R sin (4t). R is a constant.

Which of the following expressions is not a value for the average acceleration, a?

Eval Kneivel is rides up a ramp inclined at 30^o to the horizontal. He reaches the top of the ramp at height h, travelling at a speed of 80 km h^–1. He is riding into a headwind, which provides a horizontal force of 50 N.

Eval and his motorcycle have a combined mass of 200 kg. He spends 3 s in the air and lands a distance d from the base of the ramp.

Which row A to D in the table gives the correct values for h and d?

	h / m	d / m
A	13.6	32.2
B	75.9	207
C	77.5	57.7
D	10.8	56.6

A spherical ball of mass 65 kg and diameter 0.4 m is dropped from a stationary hot air balloon into a headwind of 20 m s^–1 to the horizontal. As it falls it experiences vertical drag which is calculated using the equation

D = CA

Where D = drag, ρ = density of air, v = speed of ball, C = drag coefficient and A = cross sectional area of the ball.

The density of air is 1.225 kg m^–3 and the drag coefficient of a sphere is 0.47.

The ball reaches terminal velocity.

Which row A to D in the table gives the correct values for the velocity and angle, measured to the horizontal, with which the ball strikes the ground?

	v / m s–1	θ / o
A	69.3	73.2
B	17.6 × 103	89.9
C	134	81.4
D	46.9	64.7

The graph shows the results of the required practical to determine the value of g using light gates.

Which of the following errors could have resulted in the value for g the student has obtained?

A car makes a journey starting from rest. The graph shows the acceleration of the car over time.

The initial velocity of the car is 0.

What is the distance travelled by the car?

The force of gravitational attraction between two planets is given by the equation

F = 

Where m₁ and m₂ are the masses of the two planets and r is the separation between their centres of mass. G is the gravitational constant and has value 6.67 × 10^–11 N m² kg^–2.

The magnitude of the gravitational field strength for a planet is given by

g = 

Where r = the distance from the centre of the planet and M is the mass of the planet.

An object of mass 6 kg falls from rest on each of the two planets, which have no atmospheres. On planet 1, which has a radius of 12000 km, it reaches a velocity of 20 m s^–1 after 20 m. On planet 2, which has radius of 5000 km, it falls a distance of 120 m in 10 s. 

If the gravitational force between the two planets is 37 TN, what is the distance between them?

A sphere is released and falls. Its initial acceleration reduces until it eventually begins to travel at constant terminal velocity.

Which displacement-time graph best represents the motion of the sphere?

A bullet is fired horizontally with speed v from a rifle. For a short time t after leaving the rifle, the only force affecting its motion is gravity. The acceleration of free fall is g.

Which expression gives the value of   ?

The acceleration of free fall on the Moon is one-sixth of that on Earth. On Earth it takes time t for a stone to fall from rest a distance of 2 m.

What is the time taken for a stone to fall from rest a distance of 2 m on the Moon?

A stone is thrown upwards and follows a curved path.

Air resistance is negligible.

Why does the path have this shape?

A train passes through a station at a constant speed of 20 m s^–1

A second train is at rest at the station. It begins to leave the station with a uniform acceleration of 1.0 m s^–2  just as the first train goes past.

How much time passes before the second train overtakes the first train?

The graph shows how the speed v of a sprinter changes with time t during a 100m race.

What is the best estimate of the maximum acceleration of the sprinter?

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

What is the corresponding graph of displacement against time?

In a cathode-ray tube, an electron is accelerated uniformly in a straight line from a speed of 4 × 10⁵ m s^–1 to one tenth of the speed of light over a distance of 10mm.

What is the acceleration of the electron?

A projectile is fired at an angle α to the horizontal at a speed u, as shown.

What are the vertical and horizontal components of its velocity after a time t?

Assume that air resistance is negligible. The acceleration of free fall is g.

	vertical component	horizontal component
A	u sin α	u cos α
B	u sin α + gt	u cos α
C	u sin α – gt	u cos α
D	u cos α	u sin α – gt