An insect moving along a straight line, travels in every second distance equal to the magnitude of time elapsed. Assuming acceleration to be constant, and the insect starts at t = 0. Find the magnitude of initial velocity of insect.

Distance traveled from time ‘t-1’ sec to ‘t’ sec isS = u + a2(2t-1) -----(i)from given condition S = t  ---(ii)from (i) and (ii), t = u+a2(2t-1)⇒u = a2+t(1-a)Since u and a are arbitrary constants, and they must be constant for every time.So, coefficient of t must be equal to zero.⇒1-a = 0 ⇒a = 1 for a = 1, u = 12unitInitial speed = 12 unit