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
$a_c = \frac{v^2}{r}$
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
$a_c'= \frac{v'^2}{r}= \frac{(3v)^2}{r}= 9\frac{v^2}{r}=9 a_c$
so, the centripetal acceleration increases by a factor 9.