Question

A particle moves from rest in a straight line with alternate acceleration and retardation a and a' respectively during equal intervals of time t. Find an expression for the total distance covered at the end of 2n such intervals.

Answer 1

The velocities of the particle at the middle of various successive intervals will be,

1/2 at,(a-1/2 a')t, (3/2 a- a')t, (4/2a -3/2a')t......

Hence, the total distance covered,

The term inside parenthesis is in A.P with first term being a/2 and common difference 1/2 (a - a')