Question

1. use the following position vs. time graph to answer the following:

a) what is the speed of the object between 0 and 30 minutes?
b) what is the speed of the object 30 and 45 minutes?
c) what is the average speed of the object from 0 to 45 minutes?

Explanation:

Step1: Recall speed formula

Speed $v=\frac{\Delta x}{\Delta t}$, where $\Delta x$ is the change in position and $\Delta t$ is the change in time.

Step2: Calculate speed for 0 - 30 minutes

From the graph, at $t = 0$, $x=1.5$ km and at $t = 30$ min, $x = 1.0$ km. $\Delta x=1.0 - 1.5=- 0.5$ km, $\Delta t=30$ min. So $v_1=\frac{1.5 - 1.0}{30}=\frac{0.5}{30}=\frac{1}{60}$ km/min.

Step3: Calculate speed for 30 - 45 minutes

At $t = 30$ min, $x = 1.0$ km and at $t = 45$ min, $x = 0.5$ km. $\Delta x=0.5 - 1.0=-0.5$ km, $\Delta t = 45 - 30=15$ min. So $v_2=\frac{1.0 - 0.5}{15}=\frac{0.5}{15}=\frac{1}{30}$ km/min.

Step4: Calculate average speed for 0 - 45 minutes

At $t = 0$, $x = 1.5$ km and at $t = 45$ min, $x = 0.5$ km. $\Delta x=0.5 - 1.5=-1$ km, $\Delta t = 45$ min. Average speed $v_{avg}=\frac{1.5 - 0.5}{45}=\frac{1}{45}$ km/min.

Answer:

a) $\frac{1}{60}$ km/min
b) $\frac{1}{30}$ km/min
c) $\frac{1}{45}$ km/min