Question

A bicyclist steadily speeds up from rest to 24.0 mph in 8.50s. How far did she traveled (in given units) ? (ft)What was her acceleration (in given units) ? (ft/s^2)

Answer 1

Since the bicyclist steadily speeds up means that this a uniform accelerated motion. This also means that we can use the following equations:

$a=\frac{v_f-v_0}{t}$$s=\frac{v_f+v_0}{2}t$

Before we begin we need to convert the final velocity to appropriate units, in this case ft/s. To do this we have to remember that one mile is equal to 5280 ft and on hour is equal to 3600 seconds. Then:

$24\frac{\text{ mi}}{\text{ h}}\cdot\frac{5280\text{ ft}}{1\text{ mi}}\cdot\frac{1\text{ h}}{3600\text{ s}}=35.2\text{ }\frac{\text{ ft}}{\text{ s}}$

Now that we have this.

First question:

To find the change of position (how far the cyclist traveled) we use the second formula:

$\begin{gathered} s=\frac{35.2-0}{2}(8.5) \\ s=149.6 \end{gathered}$

Therefore she traveled 149.6 ft.

Second question:

To find the acceleration we use the first formula:

$\begin{gathered} a=\frac{35.2-0}{8.5} \\ a=4.14 \end{gathered}$

Therefore the acceleration is 4.14 ft/s^2