Distance, velocity, acceleration, and rectilinear

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.

Options:

1. 5e
2. 5e²
3. e
4. None of these

Answer 1

y = t ln (5t)

y ' = t * 5/(5t) + ln(5t) = 1 + ln(5t)

the velocity is zero when 1 + ln(5t) = 0

ln(5t) = -1

5t = 1/e

t = 1/(5e)

second derivative is y'' = 5/(5t) = 1/t

the acceleration at that time is then 1/(1/(5e)) = 5e