Can't Seem To Get It Right: Solving Centripetal Acceleration Equation

[scavok]

What I'm doing seems like it should work, but I can't seem to get it right. I'm sure I'm doing the math right, but I have a feeling I'm answering something that's not being asked. I would just like some help on setting up the equation right.

A car starts from rest on a flat circular track of radius 200.1 m and accelerates tangentially at a rate of 4.79 m/s². How much time elapses before the centripetal acceleration of the car is equal in magnitude to the tangential acceleration.

I have the tangential acceleration (a_t), and radius (r).
Using the centripetal acceleration equation a_c=v²/r, I set a_c=4.79 m/s², r=200.1m, and solve for the velocity.

I then use the circular motion period equation (v=(2*pi*r)/t), plug in the velocity I just calculated, the radius of the track, and solve for time.

I get 40.61s everytime, which is incorrect.

vv I got it now. Thanks for saving my hair.

 

[andrewchang]

that's not the right equation; you should be using kinematics/rotational kinematics to find the time that it accelerates. The T in that equation is for period.

 

[quicknote]

As a scientist, it is important to double check your calculations and equations to ensure accuracy. It is possible that there may have been a mistake in the calculation or an incorrect assumption made. It is also important to make sure that the equations being used are appropriate for the problem at hand. In this case, it seems like the equations being used were correct, but there may have been a mistake in the calculations. It is also helpful to have someone else review your work to catch any errors that may have been overlooked. Overall, it is important to approach problem solving with a critical and analytical mindset to ensure the most accurate results.