An airplane flies in a horizontal circle of radius 500 m at a speed of 150 m/s. If the plane were to fly in the same 500 m circle at a speed of 300 m/s, by what factor would its centripetal acceleration change?
A) 0.25
B) 0.50
C) 1.00
D) 2.00
E) 4.00

Question

Quizplus · Accepted Answer

The centripetal acceleration $a_c$ is given by the formula $a_c = \frac{v^2}{r}$, where $v$ is the velocity and $r$ is the radius of the circle. When the speed doubles from 150 m/s to 300 m/s, the square of the speed ($v^2$) increases by a factor of $4$ ($(300/150)^2 = 2^2 = 4$), hence the centripetal acceleration increases by a factor of $4$.

An Airplane Flies in a Horizontal Circle of Radius 500