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

Answer:

Explanation:

Given

Velocity of point is given by $v=\frac{\ln t}{t}$

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

$\frac{\mathrm{d} v}{\mathrm{d} t}=\frac{\frac{1}{t}\times t-1\times \ln(t)}{t^2}$

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

$\ln (t)=1$

$t=e$

i.e. $t=2.718\ s$