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.

Answer 1

$$v(t)=s'(t)=\ln(5t)+t\cdot\frac1t=\ln(5t)+1\\a(t)=s''(t)=\frac1t$$so when \(v(t^*)=0\) we have:$$\ln(5t^*)+1=0\\\ln(5t^*)=-1\\5t^*=\frac1e\\t^*=\frac1{5e}$$so then \(a(t^*)=5e\)