Chapter 4.3, Problem 11E

To determine

To calculate:The velocity of the object.

Answer to Problem 11E

The velocity of the object is $\frac{1}{5}$ .

Explanation of Solution

Given information:An object is moving along x- axis and its position is given by,

  $x(t)={\tan }^{-1}t$ .

  $t=2$

Formula used:

  $v=\frac{dx}{dt}$........(1)

Where, v = velocity of object

x = position of object at time t

Calculation: Using the formula given in equation (1),

  $\begin{array}{l}v=\frac{dx}{dt}\\ v=\frac{d\left({\tan }^{-1}t\right)}{dt}\\ v=\frac{1}{1+t^2}\\ \text{Put}t=2,\\ v=\frac{1}{1+2^2}\\ v=\frac{1}{5}\end{array}$

So the velocity of the object is $\frac{1}{5}$ .