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AQA AS Physics Chapter 8 problem

Hey,

There's a question that I'm really struggling with it.

A rail wagon moving at a speed of 2.0m/s on a level track reached a steady incline which slowed it down to rest in 15.0s and caused it to reverse.
Calculate:
a) the distance it moved up the incline
b) its acceleration on the incline
c) its velocity and position on the incline after 20.0s

I got a & b and they both make perfect sense.
However, C's work solution doesn't make sense AT ALL.

a) S=15m
b) A= -0.13m/s/s

For c) the work solution is:
u=2m/s
a=-0.133m/s/s
t=20s
And therefore, V= -0.67m/s & S=13.4m

IT DOESN'T MAKE ANY LOGICAL SENSE to use U as 2? I mean how did you know?? I thought U is 0 because it stopped and then it will reverse down the slope, so U shall be 0 not 2m/s.

If anybody has any decent explanation, I'll be very thankful. Please. It's driving me crazy.

Reply 1

L'Evil Fish

It's the whole motion from when it started from the bottom.

Reply 2

yussefsoudan

Original post by L'Evil Fish

It's the whole motion from when it started from the bottom.

I don't get it?

Reply 3

Stonebridge

The solution takes the starting point as being the start of the question.
Bottom of slope.
Moving at 2m/s
Accel negative as in opposite direction to motion.

You are taking the start as being the top of the climb.
Both will give the answer.

Reply 4

yussefsoudan

Thanks for your response. And yes, I know that already, as I've mentioned.
My question is why is it 2 not 0? It's now which of them.
Thanks again.

Reply 5

Stonebridge

Original post by yussefsoudan

Thanks for your response. And yes, I know that already, as I've mentioned.
My question is why is it 2 not 0? It's now which of them.
Thanks again.

It's 2 because that is the initial speed at the bottom of the slope as given in the question.
As I already mentioned.
If you set up the suvat for that scenario then that is the initial speed.
The suvat solves for the whole journey from bottom to top and back down again some of the way.
You can also just apply a suvat to just the downward part of the journey. (As you suggest)
In that case the initial velocity is zero, starting at the top.

It doesn't matter which way you do it. The final answer is the same.

The difference is that applying the suvat to the downward journey you get the distance it travelled down the slope from the highest point. Acceleration is positive as it's in the direction you are measuring the distance travelled.
If you use the suvat starting from the bottom of the slope, the value you get for displacement at the end will be the distance from the starting point at the bottom up the slope to the final position. As you are measuring distance up the slope and initial velocity is up the slope and both are positive the acceleration is negative because it is in the opposite direction (down) to the one you have taken as positive (up).
The two final numerical values will be different but the final point will be the same. One answer measuring up from the bottom and the other down from the top.