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

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