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

Answer:

centripetal acceleration becomes 4 times

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:

$a_c=\frac{v^2}{r}$

where:

$a_c=$ initial centipetal acceleration

v = initial speed of the car

r = radius of the track (remains constant)

When the speed is doubled:

$a_c'=\frac{(2v)^2}{r}$

$a_c'=\frac{4v^2}{r}$

$a_c'=4\times \frac{v^2}{r}$

$a_c'=4\ a_c$

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

Answer 2

Answer:

4 TIMES

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