Two racecars are driving at constant speeds around a circular track. Both cars are the same distance away from the center of the

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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

Physics

1 answer:

Yuliya22 [3.3K] · Answer 1 · 2026-03-08T11:05:51+03:00

Response:

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

Rationale:

Centripetal acceleration occurs when an object travels in a circular route. It can be expressed as:

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

In this scenario, two race cars are moving at consistent speeds around a circular course. Both automobiles are located at an equal distance from the center, but car 2 is operating at twice the speed of car 1.

Thus,

$\dfrac{a_1}{a_2}=\dfrac{v_1^2}{v_2^2}$

1 and 2 represent the first and second cars, respectively.

$v_2=2v_1$

Consequently,

$\dfrac{a_1}{a_2}=\dfrac{v_1^2}{(2v_1)^2}\\\\\dfrac{a_1}{a_2}=\dfrac{v_1^2}{4v_1^2}\\\\\dfrac{a_1}{a_2}=\dfrac{1}{4}\\\\a_2=4\times a_1$

Therefore, car 2's acceleration is four times that of car 1.