- #1

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## Homework Statement

I took a test today and I am pretty sure I got everything right except for this one problem that was on there which I am unsure of. If I remember correctly, it went like this:

It said there was a particle of mass 2 kg moving with a speed of 5 m/s to the right. Then there was a graph that more or less looked like this one I just made:

The question asked what the final velocity was after the impulse.

## Homework Equations

I believe this is correct and relevant.

[tex]\int F dt = J = ΔP = mv_{f} - mv_{i}[/tex]

## The Attempt at a Solution

I wagered that since the impulse was equal to the area under the curve on a Force v. Time graph, that the problem could be done in this way:

[tex]J = \frac{1}{2}(base)(height)[/tex]

[tex]J = \frac{1}{2}(0.10)(10)[/tex]

[tex]J = 0.5[/tex]

[tex]J = mv_{f} - mv_{i}[/tex]

[tex]0.5 = (2)v_{f} - (2)(5)[/tex]

[tex]10.5 = (2)v_{f}[/tex]

[tex]5.25 = v_{f}[/tex]

So I said the velocity afterwards was 5.25 m/s (and part b asked the direction, which I claimed was to the right).

It's unlike any practice/hw/quiz problems we have had before and there was some equation she wrote on the board:

[tex]F_{avg}Δt = mv_{f} - mv_{i}[/tex]

Which I believe is basically what I did, I just didn't use that equation.

Did I mess up?