posted by Laila on .
super easy (I think) but I must be missing some concept...
A race car starts from rest on a circular track. The car increases its speed at a constant rate at as it goes 5.00 times around the track. Find the angle that the total acceleration of the car makes with the radius connecting the center of the track and the car at the moment the car completes its trip of 5.00 times around the circle.
Let a be the speed acceleration rate. That vector will always be tangent to the circular path. There will also be a centripetal acceleration vector that increases with time. It is pointed toward the center of the circle and has magnitude V^2/R.
The time it takes to complete 5 revolutions is
T = 10 pi R/Vav = 20 pi R/V = V/a
where V is the speed at that time and Vav is the average speed during T, which is V/2.
Therefore V^2 = 20 pi R a
a(centripetal) = V^2/R
= 20 pi a(tangential)
The angle of the total acceleration vector to the radial direction is
arctan a(tangential)/a(centripetal) = arctan [1/(20 pi)] = 0.91 degrees