Question

A point moves on the x-axis in such a way that its velocity at time t (t > 0) is given by v=ln t/t . At what value of t does v attain its maximum?

Answer 1

Step-by-step explanation:

Given

Velocity of point is given by
`v=(\ln t)/(t)`

To get maximum or minimum velocity differentiate v w.r.t t

`\frac{\mathrm{d} v}{\mathrm{d} t}=((1)/(t)* t-1* \ln(t))/(t^2)`

so
`1-\ln (t)` should be equal to zero

`\ln (t)=1`

`t=e`

i.e.
`t=2.718\ s`