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.

Respuesta :

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

[tex]a = \frac{v^2}{r}[/tex]

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

[tex]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}[/tex]

Since [tex]v_A = 2V_E \rightarrow \frac{v_A}{v_E} = 2[/tex] and [tex]r_A = r_E[/tex]

[tex]a_A / a_E = 2^2 = 4[/tex]

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