Question

A racecar is traveling in uniform circular motion around a racetrack. What happens to the centripetal acceleration of the car if the speed is doubled and the radius of the circle remains constant?

Answer 1

4 TIMES

Step-by-step explanation:

As centripetal acceleration has formula a =v^2/r. as r is constant so a is directly proportional to square of speed so square of 2 is 4 hence 4 times

Answer 2

centripetal acceleration becomes 4 times

Step-by-step explanation:

Given that a car is in the uniform circular motion on a circular track initially and then its speed is doubled.

Now as we know the equation for centripetal acceleration in a circular motion is given as:

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

where:

`a_c=` initial centipetal acceleration

v = initial speed of the car

r = radius of the track (remains constant)

When the speed is doubled:

`a_c'=((2v)^2)/(r)`

`a_c'=(4v^2)/(r)`

`a_c'=4* (v^2)/(r)`

`a_c'=4\ a_c`

i.e. centripetal acceleration becomes 4 times in the later case.