# Question on graph of Momentum vs Distance

1. Jun 5, 2013

### lionely

1. The problem statement, all variables and given/known data

Well I think the answer is d because if the acceleration is constant then the distance should increase at a steady rate hence the straight line for d.

But my teacher says different his working is shown on the side of the question. He believes the answer is A.

2. Jun 5, 2013

### Dick

Your teacher is right. Read the explanation. If the label on the horizontal axis were 'Time' instead of 'Distance' then D would be right. But it's not.

3. Jun 5, 2013

### lionely

Oh thank you.

4. Jun 5, 2013

### HallsofIvy

Staff Emeritus
You are wrong. If acceleration is constant, then velocity increases at a constant rate (that constant rate is the acceleration). The distance traveled then increases quadratically. That is A.
(Strictly speaking that implies that the distance is a quadratic function of the time: $x= (a/2)t^2$ but the momentum is $p= mv= mat$ so $t= p/ma$ and then $x= (a/2)t^2= (a/2)(p^2/m^2a^2)= (1/2m^2a)p^2$.)

(Too late again! I shouldn't have stopped to check on my dinner!)

5. Jun 4, 2015

### M. Chizoba

i dont have anything to add. i just wanted to know if that was a CAPE question paper?

6. Jun 4, 2015

Yes it was

7. Jun 4, 2015

### M. Chizoba

oh, thats cool. i am doing the physics multiple choice exam tomorrow and i saw that question which i couldn't answer. i was very surprised to see the question here so i asked.