If particle A at ${\mathrm{t}}_1=-2.0\mathrm{s}$ is at ${\mathrm{x}}_1=4.8\mathrm{cm}$, and at ${\mathrm{t}}_2=4.5\mathrm{s}$ is at ${\mathrm{x}}_2=8.5\mathrm{cm}$, what is its average velocity over this time interval? Can you calculate its average speed from these data? Why or why not?

Given data.

The initial position is $x_1=4.8\mathrm{cm}$.

The final position is $x_2=8.5\mathrm{cm}$.

The initial time is $t_1=-2.0\mathrm{s}$.

The final time is $t_2=4.5\mathrm{s}$.

You know that $\mathrm{Average}\mathrm{velocity}=\frac{\mathrm{final}\mathrm{position}-\mathrm{initial}\mathrm{position}}{\mathrm{time}\mathrm{elapsed}}$.

Now, substituting the values,

$\begin{array}{c}\mathrm{Average}\mathrm{velocity}=\frac{x_2-x_1}{t_2-t_1}\\ =\frac{8.5\mathrm{cm}-4.8\mathrm{cm}}{4.5\mathrm{s}-\left(-2.0\mathrm{s}\right)}\\ =0.57\frac{\mathrm{cm}}{\mathrm{s}}\end{array}$.

Therefore, the average velocity over the time interval is $0.57\frac{\mathrm{cm}}{\mathrm{s}}$.

No, we can’t calculate the average speed from these data.

Here, you have only the initial and final positions for the corresponding time, and you don’t know which path the particle has traveled in, from the initial to the final position.

So, you can only calculate the displacement for this time interval and not the distance for the same. Therefore, finding the average speed from this data is not possible.