Question

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

Answer 1

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

Step-by-step explanation:

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

`a=(v^2)/(r)`

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,

`(a_1)/(a_2)=(v_1^2)/(v_2^2)`

1 and 2 represent car 1 and car 2 respectively.

`v_2=2v_1`

So,

`(a_1)/(a_2)=(v_1^2)/((2v_1)^2)\\\\(a_1)/(a_2)=(v_1^2)/(4v_1^2)\\\\(a_1)/(a_2)=(1)/(4)\\\\a_2=4* a_1`

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