Two cars race around a circular track. Car A accelerates at 0.340 rad/s2 around the track, and car B at 0.270 rad/s2. They start at the same place on the track and car A lets the slower-to-accelerate car B start first. Car B starts at time t = 0. When car A starts, car B has an angular velocity of 1.40 rad/s. At what time does car A catch up to car B?
rotational motion equations
The Attempt at a Solution
I attempted to use rotational motion equations and set up
theta car A=theta car B
since they will be in the same place (theta) at the same time.
as in: omega initial A x time + 1/2 alpha A time^2 = omega initial B x time + 1/2 alpha A time^2
So: 0(t) + 1/2(.340)t^2=1.4(t)+1/2(.270)t^2
and then I solved for time using quadratic theorem and got 40 seconds but this was incorrect. Could you tell me where I went wrong?? Thanks!