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Victor Eduardo Chavel-Heredia
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Post Number: 1
 Posted on Friday, 19 October, 2012 - 12:44 pm:

Hi, I am new here, this is my first post.
I am doing A2 level Maths and one of the modules is mechanics.
Doing some homework I found I question that, although I think I know it is correct, I find a weird answer.

The question is: a particle travels with uniform deceleration of $2 ms^{-2}$ in a horizontal line. The points A and B lie on the line and AB=32 m. At time 0 the particle passes through A with velocity $12$ $m s^{-1}$ in the direction A to B.
Find:
a)The values of t when the particle is at B.
b)The velocity of the particle for each of the values of t.

I solved a) using the equation $s=at+\frac{1}{2}at^2$ and I did get a quadratic equation. I solved it and I did get $t=8$ and $t=4$

After that, I did b) using the formula $v=u+at$, which gave me $v=-4ms^{-1}$ for $t=8s$ and $v=4ms^{-1}$ for $t=4s$.

My question is: what is the interpretation of this answers? Do you actually end up with different speeds? Or is just a result of the quadratic equation?
Simon Taylor
Veteran poster

Post Number: 700
 Posted on Friday, 19 October, 2012 - 01:54 pm:

Try and visualise how the particle moves. If it is decelerating uniformly, what is its motion going to look like? More specifically, how is the particle moving the first time it goes through the point, and how is it moving the second time?
Victor Eduardo Chavel-Heredia
New poster

Post Number: 2
 Posted on Sunday, 21 October, 2012 - 03:32 pm:

I have been thinking about it, and I think now I get it.
If the particle is decelerating, when it stops moving, it would start accelerating in the other direction, so if at the beginning I said the velocity was positive when moving to the right, it would be negative when moving to the right.

So the particle would decelerate until coming to rest and then it would come back. It will pass the same point twice, therefore we get 2 times with its velocities, one of them negative.

Is that right?
Simon Taylor
Veteran poster

Post Number: 701
 Posted on Sunday, 21 October, 2012 - 10:03 pm:

Yes, you are right. It passes the point while slowing down, and when it stops it starts moving back again (with a constant acceleration to the left at all times), and passes the point going the other way.

If you want to see an example of this, roll a ball up a straight slope and watch the ball as it passes a point up and down. The speeds will be the same (or roughly at least - the slope might not be quite flat and friction might mess things up a bit).