You are driving down the road at 15 m/s you step on the gas and speed up with uniform acceleration of 2.5 m/s^2 for 0.80 seconds. If your tires have a radius of 34 cm, what is their angular displacement during this period of acceleration?

And we have the following relation between the angular displacement and the linear displacement:

Where x represent the linear displacement and the angular displacement, if we solve for we got:

Explanation:

For this case we have the following data given:

represent the initial speed

represent the acceleration

represent the time

represent the radius

First we can calculate the linear displacement with the following formula from kinematics:

And replacing we have:

And we have the following relation between the angular displacement and the linear displacement:

Where x represent the linear displacement and the angular displacement, if we solve for we got:

And that would be the angular displacement during the period of acceleration.