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 startsat t = 0. Find the magnitude of initial velocity of insect

Distance travelled from time t - 1 sec to t sec isS=u+a2(2t−1)               .......(i) from given condition S=t    ......(ii) (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.⇒ Coefficient of t must be equal to zero. ⇒ 1−a=0⇒a=1 for a=1,u=12 unit  Initial speed is 12 unit.