Barron's 2nd Edition DT Q18

Barron's Book

18) This problem poses us with a situation where a ball moves x meters in t seconds. Now, we need to find out how far it would move with twice the force applied to it. We can start by looking at the original situation, and we can create an equation for it.

Since the object is initially at rest we can rewrite this equation simpler.

Where x is distance, a is acceleration, and t is time

Now, we are told that an identical object is pushed on with double the force. Since the objects are identical, the mass will be the same for both. This means, using Newton's 2nd Law, we can find the acceleration for the second situation.

Where F is force, m is mass, and a is acceleration

Now that we know the acceleration, we can replace 'a' with '2a' and balance the equation.

Where x is displacement, a is acceleration, and t is time

Answer: D