# AS Maths - Mechanics - Constant acceleration

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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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#2

(Original post by

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.

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.

I'm thought the variables would be: s = ?, u = ?, v = 0, a =-4, t = 2

**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

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(Original post by

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.

**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.

**s = -22.5, u = 0, v = ?, t = 2**?

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(Original post by

I'm still not sure what my variables would be after reading that. Would they be:

**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**?
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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.

**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.

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#6

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Could you just walk me through how to answer part b?

**throwaway21458**)Could you just walk me through how to answer part b?

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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