Question

A particle is moving so that ist displacement s is gives as s=t^3-6t^2+3t+4 meter.its velocity at the instant when it's acceleration is zero

Answer 1

s=t³-6t²+3t+4
differentiate s with respect to t then we get velocity
v=3t²-12t+3
differentiate v with respect to t then we get acceleration
a=6t-12
now,
according to question
a=0
6t-12=0
t=2s
hence
velocity, v=3t²-12t+3
v=3*2*2-12*2+3
v= -9m/s

Answer 2

by differentiating s we get, ist v=3t^2-12t+3. again differentiating v we get, a=6t-12, where a=0. equating the values of a we get, t=2. then it's ist velocity is 3(2)^2-12(2)+3=12-24+3=-9m/s