Question

solve. 9) an automobile is traveling at 25 ft/sec. the driver applies the brakes in such a way that the velocity decreases to zero according to the relation v(t)=25 - 0.25t2, where t = time. find an equivalent expression for v(t) by factoring out a factor with a negative coefficient.

Explanation:

Step1: Identify the common - factor

We want to factor out a negative factor from \(v(t)=25 - 0.25t^{2}\). The greatest - common factor of \(25\) and \(0.25t^{2}\) with a negative coefficient is \(- 0.25\).

Step2: Factor out \(-0.25\)

\[

$$\begin{align*} v(t)&=25 - 0.25t^{2}\\ &=-0.25(- 100 + t^{2})\\ &=-0.25(t^{2}-100) \end{align*}$$

\]

Answer:

\(v(t)=-0.25(t^{2}-100)\)