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=(v_f-v_0)/(t)`
`s=(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=(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=(35.2-0)/(8.5) \\ a=4.14 \end{gathered}`

Therefore the acceleration is 4.14 ft/s^2