Question

The velocity of a falling object in a vacuum is directly proportional to the amount of time the object has been falling. If after $5$ seconds an object is falling at a speed of $90$ miles per hour, how fast will it be falling after $12$ seconds?

• A. $200mph$
• B. $216mph$
• C. $316mph$
• D. $278mph$

Answer 1

Answer: (B)

$216mph$

Because the velocity and the time spent falling are directly proportional, you can simply set the ratio of the "before" velocity and time to the "after" velocity and time.

$\frac{v_1}{w_1}=\frac{v_2}{w_2}$

$\frac{90mph}{5sec}=\frac{v_2}{12sec}$

$v_2=\frac{90\times \left(12\right)}{5}=216mph$