Maximum distance An object moves on a line with velocity \(v(t)=10 /(t+1)^{2}\) mi/hr for \(t \geq 0\). What is the maximum distance the object can travel?

Problem 45E

Maximum distance An object moves on a line with velocity v(t)= 10/(t + l)2 mi/hr for t ≥ 0. What is the maximum distance the object can travel?

Solution

Here v=

Velocity is nothing but change in distance with respect to time

So to find the maximum distance we integrate on both sides

To find the maximum distance we equate it to zero

We get

Thus at t=9 mi we get maximum distance