Question

The position of a particle moving along x axis is given by the equation, x = 2t 3 3t 2 36t where x is in metres and time t is in seconds. The acceleration of the particle at the instant (t > 0) its velocity is zero, is

Answer 1

Explanation:

x = 2t^3+3t^2-36t

after diffrentiating...

dx/dt= v =6t^2+6t-36

but given v=0

t^2+t-6=0

t^2+3t-2t-6=0

t (t+3)-2 (t+3)=0

(t+3)(t-2)=0

t=-3 (neglected)

t=2

dv/dt=a=12t+6

now acceleration at time t=2second

a=12×2+6

=30m/s^2