Question

30 POINTS

The graph shows how many inches above the ground, y, the valve on a rotating tire is for a given number of seconds x.

How many degrees is the tire turning every second?

Enter your answer in the box.

Answer 1

It takes 2 seconds for the tire to make a full revolution. This is evident from the plot - the curve has a period of length 2.

A full revolution of the tire is a turn of 360 degrees.

So the tire turns at a rate of (360 degrees)/(2 seconds) = 180 degrees/second.

Answer 2

180 degrees per second.

Explanation:

We have been given a graph that shows the distance covered by a tire or angular velocity of a tire with respect to the number of seconds (x).

Since we know that a tire is a circle and the measure of all the angles of a circle equals to 360 degrees.

We can see from our given graph that the tire completes one rotation in 2 seconds (2.5-0.5), so the distance covered by tire in two seconds will be 360 degrees. This means that the tire turns 360 degrees in each 2 seconds.

`\text{Degrees turned by tire in 2 seconds}=\frac{360^o}{2\text{ seconds}}`

As we are asked to find the degree change by tire per second so we will find the unit rate such that we will have 1 in our denominator. By dividing our numerator and denominator by 2 we will get,

`\text{Degrees turned by tire in every second}=\frac{180^o}{\text{ second}}`

Therefore, the tire is turning 180 degrees per second.