A particle P travels in the positive direction along a straight line with constant acceleration. P travels a distance of 52 m during the 2nd second of its motion and a distance of 64 m during the 4th second of its motion.

(a) Find the initial speed and the acceleration of P.

(b) Find the distance travelled by P during the first 10 seconds of its motion.

A bus moves from rest with constant acceleration for 12 s. It then moves with constant speed for 30 s before decelerating uniformly to rest in a further 6 s. The total distance travelled is 585 m.

(a) Find the constant speed of the bus.

(b) Find the magnitude of the deceleration.

A cyclist travels along a straight road with constant acceleration. He passes through points A, B and C. The cyclist takes 2 seconds to travel along each of the sections AB and BC and passes through B with speed 4.5 m s^-1. The distance AB is \(\frac{4}{5}\) of the distance BC.

(a) Find the acceleration of the cyclist.

(b) Find AC.

A car travels along a straight road with constant acceleration. It passes through points P, Q, R and S. The times taken for the car to travel from P to Q, Q to R and R to S are each equal to 10 s. The distance QR is 1.5 times the distance PQ. At point Q the speed of the car is 20 m s^-1.

(i) Show that the acceleration of the car is 0.8 m s^-2.

(ii) Find the distance QS and hence find the average speed of the car between Q and S.

A car moves in a straight line with initial speed \(u \text{ m s}^{-1}\) and constant acceleration \(a \text{ m s}^{-2}\). The car takes 5 s to travel the first 80 m and it takes 8 s to travel the first 160 m. Find \(a\) and \(u\).

A particle P moves in a straight line ABCD with constant acceleration. The distances AB and BC are 100 m and 148 m respectively. The particle takes 4 s to travel from A to B and also takes 4 s to travel from B to C.

1. Show that the acceleration of P is 3 m s^-2 and find the speed of P at A.
2. P reaches D with a speed of 61 m s^-1. Find the distance CD.

A car travels along a straight road with constant acceleration. It passes through points A, B, and C. The car passes point A with velocity 14 m s^-1. The two sections AB and BC are of equal length. The times taken to travel along AB and BC are 5 s and 3 s respectively.

(i) Write down an expression for the distance AB in terms of the acceleration of the car. Write down a similar expression for the distance AC. Hence show that the acceleration of the car is 4 m s^-2.

(ii) Find the speed of the car as it passes point C.

A particle P moves in a straight line ABCD with constant deceleration. The velocities of P at A, B, and C are 20 m/s, 12 m/s, and 6 m/s respectively.

1. Find the ratio of distances AB : BC.
2. The particle comes to rest at D. Given that the distance AD is 80 m, find the distance BC.

A car travels in a straight line with constant acceleration \(a \text{ m s}^{-2}\). It passes the points \(A, B\) and \(C\), in this order, with speeds \(5 \text{ m s}^{-1}\), \(7 \text{ m s}^{-1}\) and \(8 \text{ m s}^{-1}\) respectively. The distances \(AB\) and \(BC\) are \(d_1 \text{ m}\) and \(d_2 \text{ m}\) respectively.

1. Write down an equation connecting
   1. \(d_1\) and \(a\),
   2. \(d_2\) and \(a\).
2. Hence find \(d_1\) in terms of \(d_2\).