Question

You and your friend are racing cars on a circular track that has a radius of 90 m. While you are stopped, your friend drives by you at a angular speed of .13 rad/s. You begin to accelerate at a rate of 3.0 m/s2 the instant they pass you. How long does it take you to catch up to your friend?

Answer 1

It takes you 8.16 seconds to catch up to your friend.

First, find the linear speed of your friend at the time you start moving:

v = ωr = (0.13 rad/s)(90 m) = 11.7 m/s

Then, use the equation for the distance traveled under uniform acceleration to find the distance you have to travel to catch up to your friend:

d = vt + 0.5at^2

where d = 90 m (the track's radius),

v = 11.7 m/s (your friend's initial speed),

a = 3.0 m/s^2 (your acceleration), and

t is the time it takes you to catch up to your friend.

Solving for t, we get:

t^2 = 2d/a + 2v/a = (2)(90 m)/(3.0 m/s^2) + (2)(11.7 m/s)/(3.0 m/s^2) = 66.67 s

t = √66.67 s = 8.16 s

So it takes you 8.16 seconds to catch up to your friend.