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Click Play to watch the video. Answer the ungraded questions in the video and the graded follow-up questions at right. Part A Two racecars are driving at constant speeds around a circular track. Both cars are the same distance away from the center of the track, but car 2 is driving twice as fast as car 1. The acceleration of car 2 is ___________ the acceleration of car 1. a) equal to b) a quarter of c) twice d) four times e) half of

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skyluke89

Answer:

d) four times

Explanation:

The centripetal acceleration of an object in circular motion is defined by the equation

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

where

v is the speed of the object

r is the radius of the circular path

Calling [tex]v_1[/tex] the speed of car 1, its acceleration is:

[tex]a_1 = \frac{v_1^2}{r}[/tex]

While the acceleration of car 2 is

[tex]a_2 = \frac{v_2^2}{r}[/tex]

However, we know that the speed of car 2 is twice as that of car 1:

[tex]v_2 = 2v_1[/tex]

So substituting into the previous equation,

[tex]a_2 = \frac{(2v_1)^2}{r}=4\frac{v_1^2}{r}=4a_1[/tex]

So, acceleration of car 2 is 4 times the acceleration of car 1.

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