Question

A race car starts from rest on a circular track of radius 490 m. The car's speed increases at the constant rate of 0.430 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
m/s

(b) the distance traveled
m

( c) the elapsed time
s

Answer 1

Initial speed u = 0

Radius r = 490 m

Accleration a = 0.43 m/s ²

centripetal accelerations a ' = tangential accelerations a "

a ' and a " are perpendicular to each other.

So, a = [a ' ² + a " ²]

         = [a ' ² + a ' ²]

         = [2a ' ² ]

         = 2 x a '

From this centripetal accleration a ' = a / 2

                                                    = 0.43 / 2

                                                    = 0.304 m/s ²

We know a ' = v ² / r

From this speed of the race car v = [a ' r]

                                                = 148.98

                                                = 12.2 m/s

(b).Distance traveled S = ?

From the relation v ² - u ² = 2aS

From this S = [v ² - u ² ]/2a

                 = 173.2 m

(c).Elapsed time t = S/ v

                           = 14.2 s