Question

the velocity,v, of a falling object is directly proportional to the square of the time t, that it has been in free fall. An object that has been in free fall for 6 seconds has a velocity of 576 feet per second. Determine the velocity of an object that has been falling for four seconds.

Answer 1

The phrase "directly proportional to the square" means that y = k times x^2, where k is called the "constant of proportionality." In this case, v = k t^2. You have a t and a v in the example. Use them to find k. Since k never changes (constant), you'll use it for the next half of the problem.

Now you are asked for v when t = 4. Remember that you know k. Plug in and do the arithmetic. That's it. The key is understanding the phrase I defined at the top of this post.