Question

Assume that the car at point A and the one at point E are traveling along circular paths that have the same radius. If the car at point A now moves twice as fast as the car at point E, how is the magnitude of its acceleration related to that of car E.

Answer 1

Answer:

The magnitude of car A acceleration is 4 times that of car E

Explanation:

Assuming they are traveling at a constant speed. Their (centripetal) acceleration is as the following

$a = \frac{v^2}{r}$

where v is the (linear) velocity and r is the radius. We can use this to calculate their ratio

$a_A / a_E = \frac{v_A^2/r_A}{v_E^2/r_E} = \left(\frac{v_A}{v_E}\right)^2\frac{r_E}{e_A}$

Since $v_A = 2V_E \rightarrow \frac{v_A}{v_E} = 2$ and $r_A = r_E$

$a_A / a_E = 2^2 = 4$

So the magnitude of car A acceleration is 4 times that of car E