Physics help anyone?

Question

A race car starts from rest on a circular track of radius 340m. The car's speed increases at the constant rate of 0.41m/s^2. At the point where the magnitudes of the centripetal & tangential accelerations are equal, find the speed of the race car (in units of m/s).

What is the distance traveled?

What is the elapsed time?

Can anyone at least get me started on this problem? Like maybe tell me which formulas to use? The part that most confuses me is the whole 'centripetal & tangential accelerations are equal' thing...

Answer 1

I can give you a little bit of a boost so to speak on this problem as it sounds like you don't want the entire solution.

Firstly, the tangential acceleration component is simply the rate of increase of the cars speed. That is to say:

at = 0.41 m/s^2.

When the car is going around the corner it will always be accelerating tangent to the radius it is turning around. Sounds a little confusing, but if you draw out the car and how it is turning you should be able to see what I am saying.

Now i am sure you have seen the equation for centripetal acceleration. This is simply:

ac = V^2 / r

Now the question is asking you to find the velocity (V) when the tangential and centripetal accelerations are equal. So you want to find where:

at = ac

Notice you have everything in the two equations except for V. Just set them equal to eachother and solve for V. If you are still having trouble just send me a mail and I can elaborate for you.