Average speed in a full circle

Question a)

Data

Travels a full circumference of radius r=4m.
Elapsed time Δt=1,5 s. Δt=1,5 sg.

Resolution

To solve we will use the equation that establishes that average speed is the ratio of distance traveled (Δs) and the time that it takes to do it (Δt):

Looking at the equation we can see that we know how long it takes to finish (Δt = 1.5 s), but we need to know the distance traveled in this time. However, we know that it moves along a circumference and that the length of a circumference is given by the following expression:

$$l=2·\pi ·r$$

Substituting r=4 m,

$$\begin{gathered} \Delta s=2·\pi ·4 m\Rightarrow \\ \boxed{\Delta s=25.13 m} \end{gathered}$$

Once we know s, we can calculate the average speed with the previous equation:

$$\begin{gathered} V_{\mathrm{avg}}=\frac{25.13}{1.5}\Rightarrow \\ \boxed{V_{\mathrm{avg}}=16.75 \text{m/sg}} \end{gathered}$$

Question b)

Data

The same as in the previous question

Resolution

Average velocity is given by the following expression:

where $∆\overrightarrow{r}$ is the displacement. Since the body does a full circle, once the 1.5 seconds have passed the body will be back to the starting point and there will be no displacement at all, that is, $∆\overrightarrow{r}=0·\overrightarrow{i}+0·\overrightarrow{j} m =\hspace{0.17em}0 m$. Therefore, the average velocity vector for this case is $v_{avg}=0·\overrightarrow{i}+0·\overrightarrow{j} m$ and its magnitude will be 0. Then:

$$\boxed{\left|\overrightarrow{V_{\mathrm{avg}}}\right| = 0 m}$$