Problem: How long does it take an object moving at 3 meters/second to move 12 meters?
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Solution: Moving at 3 meters every second, we would go 3 meters in 1 second, 6 meters in 2 seconds, 9 meters in 3 seconds, . . ., 12 meters in 12 seconds. It helps to visualize this. Having visualized the situation it becomes clear that we can determine the number of seconds if we divide the 12 meters by 3 meters per second.
Generalized Response: Since distance `dist is equal to the product of speed and time interval,
`dist = v `dt,
the time interval must be
`dt = `dist / v
. This is a simple algebraic rearrangement of `dist = v `dt (we just divide both sides by v), and it is also common sense: if we moved 6 meters at 2 meters per second we would require 3 seconds; this is obvious if we think about it, and we observe that when the numbers are obvious we naturally divide the distance by the time interval. We do the same thing when the numbers aren't obvious.
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Figure description:
The image below shows a 'triangle' connecting vAve, `dt and `ds. This triangle indicates that vAve,`dt and `ds are connected in such a way that the value of any of the three quantities can be found from the values of the other two.
We know that `ds = vAve `dt. If we divide both sides of this equation by `dt and reverse sides we get
vAve = `ds / `dt.
If we divide both sides by vAve and reverse sides we get
`dt = `ds / vAve.
These relationships are indicated on the diagram.
This specific problem could be solved by direct reasoning. We can also get the answer using the relationship `dt = `ds / vAve, with the given `ds and vAve.
