Question

A car is moving in uniform circular motion. If the car's speed were to double to keep the car moving with the same radius, the acceleration would

increase by a factor of 2
increase by a factor of 4
decrease by a factor of 2
decrease by a factor of 4

Answer 1

Increase by a factor of 4.

Step-by-step explanation:

The acceleration of a car moving with speed v in a circle of radius R is given by:

`a=(v^2)/(R).`

Now if we double the speed
`v` in the equation above, it becomes
`2v`. Thus:

`a=(v^2)/(R)\:\: {\rightarrow}\:\: a_n=((2v)^2)/(R)=4(v^2)/(R)=4a.`

Therefore the acceleration is increased by a factor of 4.