Radius of the path of an accelerating object in uniform Circular motion

[Runaway]

Homework Statement

A 2 kg car travels in a flat circle. At
a certain instant the velocity of the car is
24 m/s West and the total acceleration of the
car is 9 m/s
2
at 53 degrees
North of West.

What is its radius?
Answer in units of km.

Homework Equations

F=ma
w=(2pi)/T
a= w^2 r
v=wr

The Attempt at a Solution

I have no Idea where to start. But, I do know that it is accelerating because its velocity is not at a right angle to its total acceleration.

 

[tiny-tim]

Hi Runaway!

(have a pi: π and an omega: ω and try using the X² icon just above the Reply box )

… I do know that it is accelerating because its velocity is not at a right angle to its total acceleration.

if it's moving in a circle with speed v, its components of acceleration are mv²/r radially inward, and dv/dt tangentially forward

 

[Runaway]

I don't follow, what equation am I supposed to take the derivative of, and when I do, won't I end up with a equation in terms of t, which isn't stated?
I'm in an algebra and trig. based physics class, so we haven't really used calculus, but I am in a calculus class right now, and we are learning how to take implicit derivatives. So I think I can handle doing the derivative, if there isn't another way to solve the problem.

 

[tiny-tim]

Hi Runaway!

You don't have to differentiate or integrate anything, the question doesn't ask you for v, it only asks for the radius.

You know the total acceleration is at 37° to the radius, so call the radius r and find two different equations for the radial (centripetal) acceleration.

 

[Runaway]

Thanks for your help Tim, I only read your post at a glance and saw dv/dt, which made me think that I had to use that to find the answer, but now I figured it out.