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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. 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. twice half of equal to four times a quarter of

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Answer:

The acceleration of car 2 is four times of the acceleration of car 1.

Explanation:

The centripetal acceleration of the object is possessed when it moves in a circular path. It is given by :

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

In this case, two race cars 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.

So,

[tex]\dfrac{a_1}{a_2}=\dfrac{v_1^2}{v_2^2}[/tex]

1 and 2 represent car 1 and car 2 respectively.

[tex]v_2=2v_1[/tex]

So,

[tex]\dfrac{a_1}{a_2}=\dfrac{v_1^2}{(2v_1)^2}\\\\\dfrac{a_1}{a_2}=\dfrac{v_1^2}{4v_1^2}\\\\\dfrac{a_1}{a_2}=\dfrac{1}{4}\\\\a_2=4\times a_1[/tex]

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

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