Question

For a particle moving in a straight line the displscement of the particle at time is given by s = t3-6t2 +3t+7what is the velocity when its acceleration is zero

Answer 1

s=t³-6t²+3t+7

derivative both side woth respect to 't'

ds/dt =d/dt(t³-6t²+3t+7)

=3t²-12t+3

again derivative ,

d²s/dt²=d/dt(3t²-12t+3)

=6t-12

given acceleration =d²s/dt²=0

6t-12=0

t=2

v=ds/dt =3t²-12t+3

put t=2

v=3×(2)²-12×2+3

v=12-24+3=-9

let +ve

v=9m/sec