Question

Problem: an amusing park ride travels up and down. The vertical position of the ride in meters over time is shown below. Questions : 1. What is the displacement of the ride between 16 s and 24 s ? 2. What is the distance traveled by the ride between 16 s and 24 s?

Answer 1

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

Part A. The displacement of a particle in a position vs time graph is given by the absolute value of the final and initial position, like this:

`d=\lvert{p_f-p_0}\rvert`

Where:

`p_f,p_0=\text{ final and initial positions}`

The final and initial position can be read in the graph at the times "t = 24s" and "t = 16s", like this:

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

`d={-6m-0}m={-6m}`

Therefore, the displacement is -6 meters.

Part B. We are asked to determine the distance traveled between 16s and 24s. To do that we will add the absolute values of the displacement from 16s to 20s and from 20s to 24s:

`s=\lvert{d_(16-20)}\rvert+\lvert{d_(20-24)}\rvert`

The displacements are determined using the difference between the initial and final positions:

`s=\lvert{-15m-0m}\rvert+\lvert{-6m-(-15m})\rvert`

Solving the operations:

`s=\lvert{-15m}\rvert+\lvert{9m}\rvert=15m+9m=24m`

Therefore, the total distance is 24 meters.