Constant acceleration formulae

A car moves, in a straight line on a horizontal road, from a point A to a point B

The distance AB is 225 metres.

At the point B, the velocity of the car is 30 m s^–1

The car is modelled as having a constant acceleration of 2 m s^–2

Show that the car starts from rest at point A

The car continues to move past the point B in the same straight line.

Explain why the model would eventually become invalid.

A ball falls freely towards the Earth.

The ball passes through two different fixed points M and N before reaching the Earth’s surface.

At M the ball has velocity u m s¹

It can be assumed that:

the motion is due to gravitational force only

the acceleration due to gravity remains constant throughout.

Show that the time taken for the ball to travel from M to N is seconds.

Point M is h metres above the Earth.

Fully justify your answer.

In this question use = 98 m s²

Nell and her pet dog Maia are visiting the beach.

The beach surface can be assumed to be level and horizontal.

Nell and Maia are initially standing next to each other.

Nell throws a ball forward, from a height of 1.8 metres above the surface of the beach, at an angle of 60 above the horizontal with a speed of 14 m s¹

Exactly 0.2 seconds after the ball is thrown, Maia sets off from Nell and runs across

Maia catches the ball when it is 0.3 metres above ground level as shown in the diagram below.

Find a

A car is travelling along a straight horizontal road with initial velocity u m s¹

Express a in terms of u.

Circle your answer.

Two particles, P and Q, move in the same horizontal plane.

Particle P is initially at rest at the point with position vector (4i 5j) metres and moves with constant acceleration (3i 4j) m s²

Particle Q moves in a straight line, passing through the points with position vectors

P and Q are moving along parallel paths.

Show that c 13

Find an expression for the position vector of P at time t seconds.

Hence, prove that the paths of P and Q are not collinear.

In this question use 9.8 m s²

A rough wooden ramp is 10 metres long and is inclined at an angle of 25 above the horizontal. The bottom of the ramp is at the point O.

A crate of mass 20 kg is at rest at the point A on the ramp.

The crate is pulled up the ramp using a rope attached to the crate.

Once in motion, the rope remains taut and parallel to the line of greatest slope of the

The tension in the rope is 230 N

The crate accelerates up the ramp at 1.2 m s²

Find the coefficient of friction between the crate and the ramp.

The crate takes 3.8 seconds to reach the top of the ramp.

Find the distance OA.

Other than air resistance, state one assumption you have made about the crate in answering part (b)(i).

A ball is released from a great height so that it falls vertically downwards towards the surface of the Earth.

Using a simple model, Andy predicts that the velocity of the ball, exactly 2 seconds

Show how Andy has obtained his prediction.

t seconds after being released from rest is

Find an expression for v in terms of t.

Comment on the value of v for the two models as t becomes large.

Two skaters, Jo and Amba, are separately skating across a smooth, horizontal surface of ice.

Both are moving in the same direction, so that their paths are straight and are parallel to each other.

Jo is moving with constant velocity (28i 96j) m s¹

At time t 0 seconds Amba is at position (2i 7j) metres and is moving with a

constant.

Verify that k 08

Find the position vector of Amba when t 4

At both t 0 and t 4 there is a distance of 5 metres between Jo and Amba’s positions.

Determine the shortest distance between their two parallel lines of motion.

Fully justify your answer.

Two particles A and B are released from rest from different starting points above a horizontal surface.

A is released from a height of h metres.

B is released at a time t seconds after A from a height of kh metres, where 0 k 1

Both particles land on the surface 5 seconds after A was released.

Assuming any resistance forces may be ignored, prove that

Fully justify your answer.

Block A, of mass 0.2 kg, lies at rest on a rough plane. The plane is inclined at an angle to the horizontal, such that tan

A light inextensible string is attached to A and runs parallel to the line of greatest slope until it passes over a smooth fixed pulley at the top of the slope.

The other end of this string is attached to particle B, of mass 2 kg, which is held at rest so that the string is taut, as shown in the diagram below.

B is released from rest so that it begins to move vertically downwards with an

Show that the coefficient of friction between A and the surface of the inclined plane is 0.17

In this question use 9.81 m s²

When A reaches a speed of 0.5 m s¹ the string breaks.

Find the distance travelled by A after the string breaks until first coming to rest.

State an assumption that could affect the validity of your answer to part (b)(i).

In a school experiment, a particle, of mass m kilograms, is released from rest at a point h metres above the ground.

At the instant it reaches the ground, the particle has velocity v m s¹

Show that

A student correctly used h 18 and measured v as 20

The student’s teacher claims that the machine measuring the velocity must have been faulty.

Determine if the teacher’s claim is correct.

Fully justify your answer.

A garden snail moves in a straight line from rest to 1.28 cm s¹, with a constant acceleration in 1.8 seconds.

Find the acceleration of the snail.

Circle your answer.

A buggy is pulling a roller-skater, in a straight line along a horizontal road, by means of a connecting rope as shown in the diagram.

The combined mass of the buggy and driver is 410 kg A driving force of 300 N and a total resistance force of 140 N act on the buggy.

The mass of the roller-skater is 72 kg A total resistance force of R newtons acts on the roller-skater.

The buggy and the roller-skater have an acceleration of 0.2 m s²

Find R.

Find the tension in the rope.

State a necessary assumption that you have made.

The roller-skater releases the rope at a point A, when she reaches a speed of 6 m s¹

She continues to move forward, experiencing the same resistance force.

The driver notices a change in motion of the buggy, and brings it to rest at a distance of 20 m from A.

Determine whether the roller-skater will stop before reaching the stationary buggy.

Fully justify your answer.

Explain the change in motion that the driver noticed.