A race car starts from rest on a circular track of radius 438 m. The car's speed increases at the constant rat

Question

A race car starts from rest on a circular track of radius 438 m. The car's speed increases at the constant rate of 0.390 m/s2. At the point where the magnitudes of the centripetal and tangential accelerations are equal, find the following.

(a) the speed of the race car

(b) the distance traveled

(c) the elapsed time

once again any help is great! thank u so much!

Answer 1

The normal force is wt. The accel is 9.81 m/s/s.

The centripetal acceleration is found from the equation;

accel=w^2 r

w are the radians per second

(there are two*pi radians  in one complete circle)

9.81 m/s/s=w^2 X 438 m

solve for w and you get

w =0.14966 radians/sec

a)

Velocity for this would be found from the equation;

v=wr

v=0.14966 rad/sec X 438 m = 65.5 m/s

c) elapsed time is found from the equation

v=at

65.5 m/s = 0.390 m/s/s X time

solve for time and you get

time= 168.1 seconds

b) distance traveled = 1/2 a t^2

                                    = 1/2 (.390)(168.1)^2

5510 meters