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. (4 points)

5e

5e2

e

None of these

Answer 1

The particle's velocity is given by the derivative of its position:

`s'(t)=\ln5t+t\frac5{5t}=\ln5t+1`

which will be 0 when

`\ln5t+1=0\implies\ln5t=-1\implies5t=e^(-1)\implies t=\frac1{5e}`

The acceleration is given by the second derivative, so we have

`s''(t)=\frac5{5t}=\frac1t`

and at
`t=\frac1{5e}`, the acceleration will be

`s''\left(\frac1{5e}\right)=\frac1{\frac1{5e}}=5e`