Relationship between speed, distance, and time

In summary, the task is to compare the distances fallen and impact velocities of two objects dropped for different amounts of time. By reasoning it out, it can be determined that the second object will fall 9 times farther and at 3 times the speed. To formalize this, the equations d = v(t) and d = v(3t) can be used for the first and second objects respectively. From here, further calculations and manipulation of these equations can be done to compare the distances and velocities more precisely.
  • #1
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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!
 
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  • #2
cvc121 said:

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.
 

1. What is the formula for calculating speed?

The formula for calculating speed is: speed = distance/time. This means that speed is equal to the distance traveled divided by the time it took to travel that distance.

2. How does an increase in speed affect the distance traveled?

An increase in speed will result in a greater distance traveled in the same amount of time. This is because speed is directly proportional to distance, meaning that as speed increases, distance also increases.

3. Is there a relationship between distance and time when calculating speed?

Yes, there is a direct relationship between distance and time when calculating speed. As distance increases, time also increases, resulting in a lower speed. Similarly, as distance decreases, time also decreases, resulting in a higher speed.

4. How can I calculate the time it takes to travel a certain distance at a given speed?

To calculate the time it takes to travel a certain distance at a given speed, you can use the formula: time = distance/speed. This means that time is equal to the distance traveled divided by the speed at which you are traveling.

5. Can speed, distance, and time all be measured in different units?

Yes, speed, distance, and time can all be measured in different units. For example, speed can be measured in miles per hour, distance can be measured in kilometers, and time can be measured in seconds. However, when using these units in calculations, they must be converted to the same unit for accurate results.

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