Calculating Acceleration of a Moving Car

[alex81388]

Homework Statement

A car moving at a speed of 34 m/s enters a curve that describes a quarter turn of radius 117 m. The driver gently applies the brakes, giving a constant tangential deceleration of magnitude 1.2 m/s2. Just before emerging from the turn, what is the magnitude of the car's acceleration?

Homework Equations

w=radians/sec
f=frequency=rev/sec
T=period

w=2(pi)/T=2(pi)(f)
a=(w^2)(r)

The Attempt at a Solution

f = (34m/s)/(2(pi)(117)= 0.0463 revolutions/sec ... the quarter turn should not be relevant at this point because this is just speed.
w=2(pi)f= 0.291 radians/second ... still just speed... right?

a = w^2 * r = (0.291)^2 * 117 = 9.91 m/s^2 ... now i tried talked a fourth of this, and then subtracting the 1.2m/s/s deceleration... that didn't work. neither did taking the 1.2 off of it without taking a fourth.

I can't figure out what I am missing or doing wrong :(

Thanks for any help in advance!
-Alex

 

[dynamicsolo]

You've got two accelerations to consider here. One is the tangential acceleration, which you are given. The second is the centripetal acceleration, which is (omega^2)·r or (v_tangential^2)/r . That is directed radially toward the center of the curve, so it is perpendicular to the tangential acceleration. It looks like the problem asks for the total acceleration at the end of the quarter-circle, so you are going to need to find the (linear or angular) speed of the car at that point. You then would use the Pythagorean Theorem to find the total acceleration from the two components.