## Statement

A body does a full circle of 4-meter radius in 1.5 seconds. Calculate:

a) the average speed.

b) the average velocity.

## Solution

**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:

$$l=2\xb7\pi \xb7r$$

Substituting r=4 m,

$$\Delta s=2\xb7\pi \xb74m\Rightarrow \phantom{\rule{0ex}{0ex}}\overline{)\Delta s=25.13m}$$

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

$${V}_{\mathrm{avg}}=\frac{25.13}{1.5}\Rightarrow \phantom{\rule{0ex}{0ex}}\overline{){V}_{\mathrm{avg}}=16.75\text{m/sg}}$$

**Question b)**

**Data**

The same as in the previous question

**Resolution**

Average velocity is given by the following expression:

where $\u2206\overrightarrow{r}$ 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, $\u2206\overrightarrow{r}=0\xb7\overrightarrow{i}+0\xb7\overrightarrow{j}m=\hspace{0.17em}0m$. Therefore, the average velocity vector for this case is ${v}_{avg}=0\xb7\overrightarrow{i}+0\xb7\overrightarrow{j}m$ and its magnitude will be 0. Then:

$$\overline{)\left|\overrightarrow{{V}_{\mathrm{avg}}}\right|=0m}$$