Either the prof or I am crazy. What might distance/velocity be?

Question

We were asked to graph results from an experiment dealing with a projectile, and we were asked to make the X axis velocity and the Y axis distance. There are then questions about slope and time. As far as I can tell, T=v/x from the original equation, x/t=v. I find nothing about the equation flipped. I am also sure that the last time I checked, slope is rise (Y) over run (X). Is there a good reason for this madness or is he the nutty professor?

Answer 1

The professor is not the crazy one. I'm afraid that you made a mistake. Let's go through it carefully so that you'll understand what that mistake was:

As you correctly said, x/t = v. This is of course normally written the other way around, namely:

v = x/t,

because that DEFINES the velocity, as the distance x travelled, divided by the time it took. That 's why and how we can say:

"The car was moving at 60 miles per hour."

That "60 miles per hour"(60mph) was its speed. If you say

"The car was moving North-East at 60mph,"

then you're technically defining a velocity, that is both a speed AND a direction.

But let's go with what you wrote, that was:

x/t = v.

Now multiply both sides of this equation by t.

Then x = vt.

Now divide both sides by v.

Then x/v = t, that is t = x/v.

Assuming that you agree with every step taken, you MUST agree that this is the right answer.

You didn't show us your own approach, you simply stated your conclusion, so there's no way that I can pinpoint where you made your mistake. However, as you should now see, you somehow managed to invert the final result.

Live long and prosper.

Answer 2

Actually, distance/velocity = time. If you think about it, miles (distance) divided by miles/hour (velocity) = hours (time).

The slope of the graph would be the change in distance over the change in velocity, which is the time elapsed.

Answer 3

No, he's correct. If you're going to do time as velocity over distance, then the y axis should be velocity. If x/t = v, then t=x/v, not v/x ☺

Doug

Answer 4

There is no reason the data could not be graphed this way, but it is certainly not standard and if slope were referenced to x there would be two solutions for each x value.