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(m)/(s^2) \end{gathered}`

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

`2(-8.2(m)/(s^2))(34m)=-v^2_0`

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

`-557.6(m^2)/(s^2)=-v^2_0`

Now we multiply both sides by -1:

`557.6(m^2)/(s^2)=v^2_0`

Now we take the square root to both sides:

`\sqrt[]{557.6(m^2)/(s^2)}=√(v^2_0)`

Solving the operations:

`23.6(m)/(s)=v_0`

Therefore, the initial velocity is 23.6 meters per second.