# A race car starts from rest on a circular track of radius 400m . The car's speed increases at the constant rate of 0.500m/s^2 . At the point where the magnitudes of the centripetal and tangential accelerations are equal , determine the speed of the car ?

##### 1 Answer

Apr 9, 2018

Centripetal acceleration

#a_c=Romega^2=v^2/R#

where#v# is linear velocity of the object,#omega# is its angular velocity and#R# is the radius of the circle in which object moves.

Tangential acceleration

Equating the magnitudes of two and inserting value of

#v^2/400=0.500#

#=>v=sqrt(0.500xx400)=sqrt200=14.142\ ms^-1#