Relationship between speed, distance, and time

[cvc121]

Homework Statement

One object is dropped and falls for T seconds. Another object is dropped and falls for 3T seconds. Compare the distances fallen and their impact velocities, mathematically.

Homework Equations

v = d/t

The Attempt at a Solution

Just by reasoning it out, I know that the second object will fall 9 times as far and at 3 times the speed. However, I am not sure how to reason this out mathematically.

When comparing the distances fallen, I get d = v(t) for the first object and d = v(3t) for the second object. However, I can't seem to find a way to compare these equations.

Thanks! All help is very much appreciated!

 

[phinds]

Homework Statement

One object is dropped and falls for T seconds. Another object is dropped and falls for 3T seconds. Compare the distances fallen and their impact velocities, mathematically.

Homework Equations

v = d/t

The Attempt at a Solution

Just by reasoning it out, I know that the second object will fall 9 times as far and at 3 times the speed. However, I am not sure how to reason this out mathematically.

When comparing the distances fallen, I get d = v(t) for the first object and d = v(3t) for the second object. However, I can't seem to find a way to compare these equations.

Thanks! All help is very much appreciated!

Your "reasoning it out" involved numbers. How can that possibly be if you did not apply any math? My point is that you DID apply math, you just seem unsure about how to formalize it. Try writing out the equation with numbers and/or variables as appropriate and see how far you can get. It's a forum rule that you have to show some work. Clearly you have done some kind of work in your head so just follow through on it.