Find Tangential Component of Acceleration and Curvature

[CGI]

Homework Statement

Homework Equations

I know that the tangential accel is v = wr
and that Centripetal = v^2/r

The Attempt at a Solution

For A, I thought it would be straight forward if I had the radius as well as omega. I know that the distance
between A and B is 60in, but I don't think it would be safe to assume that r = 60 or half of that would it?
For B, I'm not quite sure how to go about it unfortunately

 

[TSny]

I know that the tangential accel is v = wr

Note that you wrote an equation for speed and claimed that it is an equation for tangential acceleration.

For part (a) you need to know the relationship between the tangential component of acceleration and how the speed is changing.

 

[CGI]

Oh wow I read that wrong. That was the tangential speed. Not acceleration.

Hmm.. Okay. Well I know that at B, the velocity was only half of A's.

I think Tangential Acceleration is the change in speed of a particle so in this case, 1/2..

Is that correct?

 

[TSny]

Tangential acceleration is not the change in speed. It is the rate at which the speed is changing.

As far as tangential acceleration is concerned, it makes no difference whether the road is sinuous or straight. Thus, if you imagined the curvy road straightened out to a make a straight line, the change in speed from one end to the other would be the same if the tangential acceleration on the curvy road is the same as the acceleration along the straight line. Thus, you can use what you know about one-dimensional kinematics to help you solve part (a).