Chapter 2, Problem 26P

To determine

The speed of the car just before braking.

Answer to Problem 26P

The initial speed of the car just before braking is $36\text{ m/s}$ .

Explanation of Solution

Given:

The acceleration of the car

  $a=-7.00{\text{ m/s}}^2$

The final velocity of the car

  $v=0\text{ m/s}$

Skid marks are left $92\text{ m}$ long on the highway. So, the distance the car skids before coming to rest

  $x-x_0=92\text{ m}$

Formula used:

The initial speed $v_0$ of the car is determined using the following equation of motion:

  $v^2=v_0^2+2a\left(x-x_0\right)$

Calculation:

Substitute the values of the given variables in the formula and calculate the car’s initial speed.

  $\begin{array}{c}{v}^2=v_0^2+2a\left(x-x_0\right)\\ {\left(0\text{ m/s}\right)}^2=v_0^2+2\left(-7.0{\text{ m/s}}^2\right)\left(92\text{ m}\right)\end{array}$

Therefore,

  $v_0^2=1288{\left(\text{m/s}\right)}^2$

Hence,

  $\begin{array}{c}{v}_0=\sqrt{1288{\left(\text{m/s}\right)}^2}\\ =35.9\text{ m/s}\\ \approx 36\text{ m/s}\end{array}$

Conclusion:

Thus, the initial speed of the car just before braking is $36\text{ m/s}$ .