A body moving with a constant acceleration travels the distances 3 m and 8 m respectively in 1 s and 2 s.

Calculate —

(i) the initial velocity, and

(ii) the acceleration of body.

A car travels with a uniform velocity of 25 m s^-1 for 5 s. The brakes are then applied and the car is uniformly retarded and comes to rest in further 10 s.

Find —

(i) the distance which the car travels before the brakes are applied,

(ii) the retardation and

(iii) the distance travelled by the car after applying the brakes.

A space craft flying in a straight course with a velocity of 75 km s^-1 fires its rocket motors for 6.0 s. At the end of this time, its speed is 120 km s^-1 in the same direction.

Find —

(i) the space craft’s average acceleration while the motors were firing

(ii) the distance travelled by the space craft in the first 10 s after the rocket motors were started, the motors having been in action for only 6.0 s.

A train starts from rest and accelerates uniformly at a rate of 2 m s^-2 for 10 s. It then maintains a constant speed for 200 s. The brakes are then applied and the train is uniformly retarded and comes to rest in 50 s.

Find —

(i) the maximum velocity reached,

(ii) the retardation in the last 50 s,

(iii) the total distance travelled, and

(iv)the average velocity of the train.