Kinematics

A particle is moving along a straight line. At time t seconds, the displacement, x metres, of the particle from a fixed point O on the line is given by

At time t seconds, the velocity of the particle is v m/s

Find an expression for v in terms of t

Find the least speed, in m/s, of the particle.

Differentiate 4 10t 6t²

A rocket moves vertically so that at time t seconds, the velocity, v m/s is given by

Find the time, in seconds, when the rocket stops accelerating vertically.

The vertical displacement, d metres, of the rocket at time t seconds, is given by

The rocket is launched from a height of k metres above horizontal ground. The height, in metres, above ground when the rocket is first instantaneously at rest is 20 metres.

Find the value of k

The diagram shows a sketch of the speed-time graph of part of a cyclist’s journey along a straight horizontal road.

Calculate the deceleration, in m/s², for the last 2 seconds of this part of the cyclist’s journey.

At time t = 0 seconds, the speed of the cyclist is u m/s

The cyclist travelled a total distance of 65 m in the 8 seconds.

Calculate the value of u

A particle P is moving along a straight line that passes through the point O The displacement, x metres, of P from O at time t seconds (t 0) is given by

At time t seconds, the velocity of P is v m/s

Find an expression for v in terms of t

The particle P comes to instantaneous rest at the point A

Find, in metres, the distance OA

A particle P is moving along a straight line. At time t seconds, the displacement, s metres, of P from a fixed point O on the line is given by

At time T seconds, where T 9, P is at the point A on the line.

At A, particle P instantaneously reverses its direction of motion and moves back towards O

Find the value of T

As P moves from A back towards O, the greatest speed of P is Vm/s

Find the value of V

A particle P is moving along a straight line through the fixed point O

The speed, v m/s, of P at time t seconds is given by

Complete the table of values for v 2

Give your values of v to 2 decimal places.

On the grid opposite, plot the points from your completed table and join them to form a smooth curve.

Using your curve, find an estimate, to one decimal place, for the speed of P when t = 1.75

The acceleration of P at time t seconds where 1 t 5 is a m/s²

Find an expression for a in terms of t

Using your answer to part (d), find the value of t when P has its minimum speed in

Turn over for a spare grid if you need to redraw your curve.

Only use this grid if you need to redraw your curve.

A rocket is launched from a point which is 5 m above horizontal ground.

The rocket moves vertically upwards so that at time t seconds, the height, h metres, of the rocket above the ground is given by

At time t seconds, the velocity of the rocket is vm/s and the acceleration of the rocket is am/s²

Find an expression for v in terms of t.

Find an expression for a in terms of t.

Find the time when the rocket stops accelerating upwards.

The rocket is instantaneously at rest when it is at point A.

Show that the height, in metres to one decimal place, of A above the ground is 131.2 m.

The rocket now falls vertically downwards and hits the ground.

Find the total distance, to the nearest metre, travelled by the rocket at the instant it hits the ground.