Question

A solar-powered car is traveling at constant speed around a circular track. what happens to the centripetal acceleration of the car if the speed is tripled?

Answer 1

The centripetal acceleration of the car is related to its speed by the relationship

`a_c = (v^2)/(r)`
where ac is the centripetal acceleration, v is the car's speed and r is the radius of the circular orbit.

Looking at the formula, we can see that if we triple the speed (v'=3v), the centripetal acceleration becomes

`a_c'= (v'^2)/(r)= ((3v)^2)/(r)= 9(v^2)/(r)=9 a_c`
so, the centripetal acceleration increases by a factor 9.