Rotational dynamics of two cars

[zoner7]

Homework Statement

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 let's 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?

The Attempt at a Solution

So first I calculated the time that car B accelerates before car A begins to move using acceleration of car B and its final angular velocity.

My time value is 5.185

Then I calculated the distance that car B travels until it attains an angular velocity of 1.4.

My distance is 3.629.

Then I used the linear motion equations to set the final distances of cars A and B to one another, resulting in the following equation after simplified:

1/2 Alpha(car A) t^2 - 1/2 Alpha(car B) t^2 - Omega (initial car B) t - Theta (car B).

After plugging in values, I used the quadratic equation and found a time value of 42.44 seconds.

I added the time that Car B travels before it reaches car A: 5.185 + 42.44 and found an ultimate time of 47.625.

But if I plug each the smaller time into car A's linear motion equation and the larger into Car B's, the distances are unequal...

help...?

Thank you in advance.

 

[LowlyPion]

When you plug the longer time into the slower cars equation it's changed. The proper equation for that car then has no initial conditions.

X = 1/2*.27*(47.625)² = 1/*.34*(42.44)²