Question

An object travels in a circular path at speed v and experiences a centripetal acceleration a C. What will be the object's new centripetal acceleration, if its speed is increased to 2.0v ?

Answer 1

\[\color{green}{\vec{a}_c = \frac{v^2}{R}}\] If the speed doubles, \[\color{green}{\vec{a}_{c'} = \frac{(2.0~v)^2}{R}}\] The radius of curvature, R, has not changed. Doubling the speed will cause 2.0 v to be squared in the formula. So if the speed doubles, and everything else remains the same, the centripetal acceleration will increase by a factor of 4.