Chapter 3.4, Problem 45E

To determine

To select:the values of time from given option when particle is at rest.

Answer to Problem 45E

Correct option that is time when particle is at rest is C that is $t=\frac{7}{2}$ .

Explanation of Solution

Given information:

1. Position function of the particle in terms of time $t$ is as follows

$s\left(t\right)=2+7t-t^2$

2. five given options of time are as follows

1. $t=1$ .
2. $t=2$
3. $t=\frac{7}{2}$
4. $t=4$
5. $t=5$

Formula used:

Velocity of a particle at any time $t$ that is $v\left(t\right)$ having position function $s\left(t\right)$ is as follows.

  $v\left(t\right)=\frac{d}{dt}s\left(t\right)=s^{\prime }\left(t\right)$

Calculation:

Position function of particle is $s\left(t\right)=2+7t-t^2$

Evaluate velocity of particle at any time $t$ .

  $v\left(t\right)=\frac{d}{dt}s\left(t\right)$

  $=\frac{d}{dt}\left(2+7t-t^2\right)$

  $=\frac{d}{dt}2+7\frac{d}{dt}t-\frac{d}{dt}{t}^2$

  $=0+7-2t$

  $v\left(t\right)=7-2t$

When particle is at rest , velocity will be zero that is $v\left(t\right)=0$ .

Evaluate value of $t$ for following equation

  $v\left(t\right)=0$

  $7-2t=0$

  $-2t=-7$

  $t=\frac{7}{2}$

This means for value of $t$ equal to $\frac{7}{2}$ , particle is at rest.

Hence correct option is C that is $\underset{\_}{t=\frac{7}{2}}$ .