Question

A car skids to a halt in 34 meters with an acceleration of 8.2m/s/s. Calculate the cars initial velocity.

Answer 1

We are given that a car skids 34 meters before stopping with an acceleration of 8.2 meters per second squared. To determine the initial velocity we will use the following equation of motion:

$2ax=v^2_f-v^2_0$

Since the car stops completely the final velocity is zero, therefore, we have:

$2ax=-v^2_0$

Now we replace the following values:

$\begin{gathered} x=34m \\ a=-8.2\frac{m}{s^2} \end{gathered}$

The acceleration has a negative sign because the car is decelerating. Replacing the values:

$2(-8.2\frac{m}{s^2})(34m)=-v^2_0$

Now we solve the operations on the left side of the equation:

$-557.6\frac{m^2}{s^2}=-v^2_0$

Now we multiply both sides by -1:

$557.6\frac{m^2}{s^2}=v^2_0$

Now we take the square root to both sides:

$\sqrt[]{557.6\frac{m^2}{s^2}}=\sqrt{v^2_0}$

Solving the operations:

$23.6\frac{m}{s}=v_0$

Therefore, the initial velocity is 23.6 meters per second.