How Do You Calculate the Total Acceleration of a Car on a Circular Path?

[jab2102]

Homework Statement

A car that is initially at rest moves along a circular path with a constant tangential acceleration component of 2.07 m/s2. The circular path has a radius of 48.1 m. The initial position of the car is at the far west location on the circle and the initial velocity is to the north.
(a) After the car has traveled 1/4 of the circumference, what is the speed of the car?
? m/s

(b) At this point, what is the radial acceleration component of the car?
? m/s2

(c) At this same point, what is the total acceleration of the car?
magnitude ? m/s
direction ?° east of south

Homework Equations

(final velocity)^2 = (initial velocity)^2 + 2(angular acceleration)(angle)

tangental acceleration = radius x angular acceleration

radial acceleration = (angular velocity)^2 x radius

The Attempt at a Solution

a) So what I've done for a) is first put take the tangential acceleration and get the angular acceleration from that by doing... 2.07 m/s*2 / 48.1 m = .0430
Now I try to find the Vf... (final velocity)^2 = 2(.0430)(angle) BUT I don't know what to put in for the angle. Please help and I apologize for reposting this question!
Does angle equal (48.1)x(1/4)= 12.025?
If so then Vf= 1.034

Soo.. radial acceleration = (.0430)^2 x (48.1) which = .08894

Assuming all of this is right how would I calculate the total acceleration of the car and the degrees of the direction?

 

[tiny-tim]

Welcome to PF!

Hi jab2102! Welcome to PF!

(try using the X² tag just above the Reply box )

(final velocity)^2 = (initial velocity)^2 + 2(angular acceleration)(angle)

No, v_f² = v_i² + 2as becomes either

(final velocity)²= (initial velocity)² + 2(tangential acceleration)(arc-distance)​

or

(final angular velocity)²= (initial angular velocity)² + 2(angular acceleration)(angle) ​