## Statement

difficulty

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:

Substituting r=4 m,

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

Question b)

Data

The same as in the previous question

Resolution

Average velocity is given by the following expression:

where $∆\stackrel{\to }{r}$ 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, . Therefore, the average velocity vector for this case is and its magnitude will be 0. Then:

## Formulas worksheet

These are the main formulas that you must know to solve this exercise. If you are not clear about their meaning, we recommend you to check the theory in the corresponding sections. Furthermore, you will find in them, under the Formulas tab, the codes that will allow you to integrate these equations in external programs like Word or Mathematica.

Formulas
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