Question

A car rolls down a ramp in a parking garage. The horizontal position of the car in meters over time in shown below. Questions: 1.what is the displacement of the car between 8s and 24s ? 2. What is the distance traveled by the car between 8s and 24s ?

Answer 1

We are given a graph of position vs time. We are asked to determine the following.

Part 1. We are asked to determine the displacement from 8s to 24s. To do that we will use the following formula:

$d=p_f-p_0$

Where:

$\begin{gathered} d=\text{ displacement} \\ p_f,p_0=\text{ final and initial positions} \end{gathered}$

Now, from the graph we have that the position at "t = 24s" and "t = 8s" are the following:

$\begin{gathered} p_f=9m \\ p_0=3m \end{gathered}$

Now, we substitute the values in the formula for the displacement:

$d=9m-3m=6m$

therefore, the displacement is 6 meters.

Part 2. We are asked to determine the total distance from 8s to 24s. To do that we will add the displacement from 8s to 16s and from 16s to 24s:

$s=d_{8-16}+d_{16-24}$

Now, we substitute the final and initial values of each displacement:

$\begin{gathered} s=(3m-3m)+(9m-3m) \\ \\ s=0+6m=6m \end{gathered}$

Therefore, the total distance is 6 meters.