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\textbf{Vector Functions and Curves}

\textit{\textbf{One variable functions}}
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\textbf{Question}

Show that if the scalar product of the velocity and acceleration of an
object in motion is negative (or positive) then the speed of the
object is decreasing (or increasing).

\textbf{Answer}

$$\frac{d}{dt}|\underline{v}|^2 = \frac{d}{dt}\underline{v}\bullet
\underline{v} =2\underline{v} \bullet \underline{v}$$

Speed $\it{v}=|\underline{v}|$

If $\underline{v} \bullet \underline{a} &gt; 0$ then the speed is
increasing.

If $\underline{v} \bullet \underline{a} &lt; 0$ then the speed is
decreasing.


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