Question

it was once recorded that a jaguar left skid marks with were 290 m in lenght. assuming that the jaguar skidded to a stop with a constant acceleration of -3.90 m/s^2, determine the speed of the jaguar before it began to skid.

Answer 1

Here's a graphical solution. If you plot speed vs. time, and you have constant acceleration, you get a graph similar to [skid.png].
The distance traveled during the deceleration is the area beneath the line. In this case, it's a triangle. Therefore:
\[d=\frac{1}{2}st\]
And you know the acceleration and distance traveled:
\[a=\frac{s}{t}=-3.90\]
\[d=290\]
We solve for \(t\):
\[t=\frac{s}{-3.90}\]
Substitute \(t\) to the first equation:
\[\begin{align*}
d&=\frac{1}{2}st\\
290&=\frac{1}{2}\left( \frac{s^2}{-3.90} \right)
\end{align*}\]
We can now solve for initial speed \(s\), disregard the negative sign of the acceleration:
\[s=\sqrt{(2)(290)(3.90)}\]