A car starts from rest on a curve with a radius of 150 m and accelerates at 1.50 m/s^2. How many revolutions will the car have gone through when the magnitude of its total acceleration is 3.20 m/s^2 ?

Question

A car starts from rest on a curve with a radius of 150 m  and accelerates at 1.50 m/s^2. How many revolutions will the car have gone through when the magnitude of its total acceleration is 3.20 m/s^2 ?

bobpursley · Answer

total acceleration= sqrt(1.5^2+(v^2/r)^2)

3.2^2-1.5^2=(v^2/r)^2

solve for v^2/r

then,

angvelocity^2=2*angularacceleration*angulardisplacement

(V^2/r)1/r=2*1.50/r*angulardisplacement
solve for angular displacement, divide by 2PI to get revolutions