AS Maths - Mechanics - Constant acceleration

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throwaway21458
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Question

A particle P is moving on the x-axis with constant deceleration 4 ms^-2.

At time t = 0, P passes through the origin O with velocity 14 ms^-1 in the positive direction.

The point A lies on the axis and OA = 22.5m. Find:

a) the difference between the times when P passes through A.

b) the total distance travelled by P during interval between these times.

(a)

s = 22.5, u = 14, v = ?, a = -4, t = ?

I solved this (s = ut + 1/2at^2) and got two answers for time.

t = 2.5 or t = 4.5

The difference (4.5 - 2.5) being 2 seconds.

(b)

I'm not sure how to answer this section.
I'm thought the variables would be: s = ?, u = ?, v = 0, a =-4, t = 2
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Pangol
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(Original post by throwaway21458)
Question

A particle P is moving on the x-axis with constant deceleration 4 ms^-2.

At time t = 0, P passes through the origin O with velocity 14 ms^-1 in the positive direction.

The point A lies on the axis and OA = 22.5m. Find:

a) the difference between the times when P passes through A.

b) the total distance travelled by P during interval between these times.

(a)

s = 22.5, u = 14, v = ?, a = -4, t = ?

I solved this (s = ut + 1/2at^2) and got two answers for time.

t = 2.5 or t = 4.5

The difference (4.5 - 2.5) being 2 seconds.

(b)

I'm not sure how to answer this section.
I'm thought the variables would be: s = ?, u = ?, v = 0, a =-4, t = 2
As you have t = 2, you are presumably considering the motion from the first time that P passes through A to the second time that P passes through A. Do you have any reason to think that the velocity of P is zero at the end of this motion? It might be better to consider the total displacement for this part of the motion.
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throwaway21458
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(Original post by Pangol)
As you have t = 2, you are presumably considering the motion from the first time that P passes through A to the second time that P passes through A. Do you have any reason to think that the velocity of P is zero at the end of this motion? It might be better to consider the total displacement for this part of the motion.
I'm still not sure what my variables would be after reading that. Would they be: s = -22.5, u = 0, v = ?, t = 2?
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Pangol
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(Original post by throwaway21458)
I'm still not sure what my variables would be after reading that. Would they be: s = -22.5, u = 0, v = ?, t = 2?
If you're using t = 2, then you are considering the motion from A and back to A again. Would s = -22.5? No - this is the displacement from A to O, and you are not finishing at O. You are finishing at A. What is the displacement from A to A? Similarly, I don't see how you can use an initial velocity of zero. The velocity of P is not zero either of the times when it passes through A. Best not to use either of the velocities.
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throwaway21458
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(Original post by Pangol)
If you're using t = 2, then you are considering the motion from A and back to A again. Would s = -22.5? No - this is the displacement from A to O, and you are not finishing at O. You are finishing at A. What is the displacement from A to A? Similarly, I don't see how you can use an initial velocity of zero. The velocity of P is not zero either of the times when it passes through A. Best not to use either of the velocities.
Could you just walk me through how to answer part b?
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Pangol
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(Original post by throwaway21458)
Could you just walk me through how to answer part b?
Sorry, some of the things I said earlier weren't really appropriate for the question you are trying to answer.

Your first idea - s = ?, u = ?, v = 0, a = -4, t = 2 - is really close. Although you don't say so, I assume you are considering the motion from A to the point where P stops moving. If you can find the s for this problem, then you just have to double it to answer the question. The only bit of fine-tuning that you need is that t is not 2 - that is the number of seconds required for P to g from A and back to A again. If P goes from A to the point where it stops, what value of et do you think you need?

Apologies for the earlier nonsense!
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