Determine whether the statement is true or
false. If it is true, explain why it is true. If it is false, explain why or give an example to show why it is false.
Suppose that the acceleration of $\operatorname{Car} A$ and Car $B$ along a straight road are $a_{1}(t) \mathrm{ft} / \mathrm{sec}^{2}$ and $a_{2}(t) \mathrm{ft} / \mathrm{sec}^{2}$, respectively, over the time interval $\left[t_{1}, t_{2}\right]$, where $a_{1}$ and $a_{2}$ are continuous functions with $a_{1}(t) \geq a_{2}(t)$ on $\left[t_{1}, t_{2}\right]$. Then at time $t=t_{2}$, Car $A$ will be traveling $\int_{n}^{\int_{2}}\left[a_{1}(t)-a_{2}(t)\right] d t \mathrm{ft} / \mathrm{sec}$ faster than Car $B$. (Assume that $t$ is measured in seconds.)