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

Answer:

Increase by a factor of 4.

Explanation:

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

$a=\frac{v^2}{R}.$

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

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

Therefore the acceleration is increased by a factor of 4.