Chapter 2, Problem 22SP

A car traveling at 30.0 mph uniformly accelerates up to 50.0 mph in 20.0 s. What

was its average speed in m/s? [Hint: 1 mph = 0.447 07 m/s.]

To determine

The average speed of the car, in $\text{m/s}$, traveling at $30\text{ mph}$ accelerated uniformlyup to $50\text{ mph}$ in 20.0 s.

Answer to Problem 22SP

Solution:

$17.88\text{ m/s}$

Explanation of Solution

Given data:

The initial velocity of the car is $30\text{ mph}$.

The final velocity of the car is $50\text{ mph}$.

Time taken, $t=20.0\text{s}$

And,

$1\text{mph = 0}\text{.44707 m/s}$

Formula used:

Write the expression for average speed.

$v_{av}=\frac{v_f+v_i}{2}$

Here, $v_f$ is the final velocityand $v_i$ is the initial velocity.

Explanation:

Recall the expression for average speed.

$v_{av}=\frac{v_f+v_i}{2}$

Substitute $50\text{ mph}$ for $v_f$, and $30\text{ mph}$ for $v_i$.

$\begin{array}{c}{a}_{av}=\frac{50\text{ mph}+30\text{ mph}}{2}\\ =40\text{ mph}\left(\frac{0.44707\text{ m/s}}{1\text{ mph}}\right)\\ =17.88\text{ m/s}\end{array}$

Conclusion:

The average speed of the car is $17.88\text{ m/s}$.