Question

Hint: first convert the given final speed (in mph) to find ft/s, then solve for the distance and acceleration.

Answer 1

`\begin{gathered} Dis\tan ce=149.56ft \\ Acceleration=4.14ft/s^2 \end{gathered}`

Step-by-step explanation

First, we have to find the acceleration of the bicyclist.

To do that, we apply the formula:

`a=(v-u)/(t)`

where u = initial velocity

v = final velocity

t = time

Let us convert the speed given to feet per second. To do that, multiply the speed by 1.46667:

`\begin{gathered} 24\cdot1.46667 \\ \Rightarrow35.2mph \end{gathered}`

The bicyclist started from rest, so the initial speed is 0 ft/s.

Therefore, the acceleration is:

`\begin{gathered} a=(35.2-0)/(8.5) \\ a=4.14ft/s^2 \end{gathered}`

Now, to find the distance traveled, apply the formula:

`s=ut+(1)/(2)at^2`

Therefore, the distance traveled is:

`\begin{gathered} s=(0\cdot8.5)+(1)/(2)\cdot4.14\cdot8.5^2 \\ s=(1)/(2)\cdot4.14\cdot8.5^2 \\ s=149.56ft \end{gathered}`