Question

A car rolls down a ramp in a parking garage. The horizontal position of the car in meters over time is shown below. Questions: 1. Wha is the displacement of the car between 0 s and 24 s ? 2. What is the distance traveled by the car between 0 s and 24 s ?

Answer 1

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

Part 1. To determine the displacement we will use the following formula:

`d=p_f-p_0`

Where:

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

The final position is the position at "t = 24s" and the initial position is at "t = 0s". From the graph we have:

`\begin{gathered} p_f=0 \\ p_0=12m \end{gathered}`

Now, we plug in the values:

`d=0-12m=-12m`

Therefore, the displacement is -12 meters.

Part 2. We are asked to determine the total distance from 0s to 24s. To do that we will determine the displacements from 0 to 8s, from 8s to 16s, and from 16s to 24s:

`s=\lvert{d_(0-8)}\rvert+\lvert{d_(8-16)}\rvert+\lvert{d_(16-24)}\rvert`

Now, we plug in the initial and final values:

`s=\lvert{6m-12m}\rvert+\lvert{6m-6m}\rvert+\lvert{0-6m}\rvert`

Solving the operations we get:

`s=\lvert{-6m}\rvert+\lvert{0m}\rvert+\lvert{-6m}\rvert=6m+6m=12m`

Therefore, the total distance is 12 meters.