Chapter 8, Problem 1RE

To determine

To find the distance travel by a toy car.

Answer to Problem 1RE

The toy car travel $10.42$ ft distance.

Explanation of Solution

Given:

A toy car slides down a ramp and coasts to a stop after $5$ sec. Its velocity from $t=0$ to $t=5$ is molded by $v\left(t\right)=t^2-0.2t^3$ ft/sec .

Calculation:

Since , the velocity of toy car is given by

  $v\left(t\right)=t^2-0.2t^3$ ft/sec

Also

  $\begin{array}{l}\frac{ds}{dt}=v\left(t\right)\\ ds=v\left(t\right)dt\\ \text{integrating both side}\\ {\displaystyle \underset{0}{\overset{s}{\int }}ds}={\displaystyle \underset{0}{\overset{5}{\int }}v\left(t\right)dt}\\ {\displaystyle \underset{0}{\overset{s}{\int }}ds}={\displaystyle \underset{0}{\overset{5}{\int }}\left(t^2-0.2t^3\right)dt}\\ {\left|s\right|}_0^s={\left|\frac{t^3}{3}-0.2\frac{t^4}{4}\right|}_0^5\\ s-0=\left(\frac{{\left(5\right)}^3}{3}-0.2\frac{{\left(5\right)}^4}{4}\right)-\left(\frac{{\left(0\right)}^3}{3}-0.2\frac{{\left(0\right)}^4}{4}\right)\\ s=\frac{125}{3}-\frac{125}{4}\\ s=10.42\end{array}$

Therefore, the toy car travel $10.42$ ft distance.