Question

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 ?

Answer 1

Centripetal acceleration `a_c` is given by the expression

`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 `a_t` is given to be `=0.500\ ms^-2`

Equating the magnitudes of two and inserting value of `R` we get

`v^2/400=0.500`
`=>v=sqrt(0.500xx400)=sqrt200=14.142\ ms^-1`