Question

A particle is moving along the x-axis so that its position at t ≥ 0 is given by s(t) = (t)In(5t). Find the acceleration of the particle when the velocity is first zero.
5e
5e2
e
None of these

Answer 1

position =  s(t) = (t)In(5t)

velocity = ds/dt =  t d/dt (ln (5t)) +d/dt (t) ln (5t)

              = t * 5 1/5t  + ln (5t)

          =  1 + ln (5t)

acceleration = dv/dt = d^2s/dt^2 = d/dt (1 + ln(5t))

                      =d/dt (1) + d/dt (ln 5t)

                        = 0 + 1/5t * 5

                       = 1/t

0 = 1 + ln (5t)

-1 = ln (5t)

e^-1 = 5t

1/e = 5t

1/(5e) =t

acceleration = 1/t = 1/(1/5e) = 5e

Answer: 5e