maggiehodgson
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In the two M3 questions in the attachment both say, in the solutions, that in the RHS "acceleration is in the direction of x decreasing".

In the first question the rocket is fired up and in the second the particle is falling down. How can x be decreasing in both cases?

I can imagine that the rockets is getting slower as x increases and the particle is getting faster as x decreases so I can believe that both would be -ve RHS but I just don't get the given explanations.

I do find mechanics a mystery so please explain in as simple a way as you possibly can.

Many thanks.
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ghostwalker
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(Original post by maggiehodgson)
In the two M3 questions in the attachment both say, in the solutions, that in the RHS "acceleration is in the direction of x decreasing".

In the first question the rocket is fired up and in the second the particle is falling down. How can x be decreasing in both cases?

I can imagine that the rockets is getting slower as x increases and the particle is getting faster as x decreases so I can believe that both would be -ve RHS but I just don't get the given explanations.

I do find mechanics a mystery so please explain in as simple a way as you possibly can.

Many thanks.
In each case x increasing is upwards, and acceleration is due solely to gravity and is downwards, hence in the direction of x decreasing.

I have to say their solutions are not very well explained - not impressed.
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maggiehodgson
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Yep. Makes sense now. Took a while to sort it out in my head, flipping between understanding and then questioning it all over again, but it's settled down now into getting it.

Thanks
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atsruser
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(Original post by maggiehodgson)
In the two M3 questions in the attachment both say, in the solutions, that in the RHS "acceleration is in the direction of x decreasing".

In the first question the rocket is fired up and in the second the particle is falling down. How can x be decreasing in both cases?

I can imagine that the rockets is getting slower as x increases and the particle is getting faster as x decreases so I can believe that both would be -ve RHS but I just don't get the given explanations.

I do find mechanics a mystery so please explain in as simple a way as you possibly can.

Many thanks.
This may or may not help but ..

You need to bear in mind that in a 1D mechanics problem, you have 3 vectors to consider, namely displacement x, velocity v =\frac{dx}{dt} and acceleration a = \frac{dv}{dt}=\frac{d^2x}{dt^2}.

Each of these vectors can point either up or down *independently* (in a vertical problem). Note that by Newton II, F=ma, then a always points in the direction of the force producing the acceleration. So in a problem with gravity, the acceleration will always point toward the Earth i.e. downwards.

However, the velocity vector may at one time point upwards (e.g. for a stone been thrown into the sky) or downwards (e.g. for a stone that's falling back to Earth). All of the time, though, the a vector points downwards.

Also the displacement vector can point up or down - up if the particle is a stone thrown into the air, down if it's a stone falling into a well (i.e. below the Earth's surface, where we usually put the origin)

And of course, you distinguish "up" vectors from "down" vectors in the algebra, by making "up" vectors +ve, and "down" vectors -ve, or vice versa.
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maggiehodgson
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Thanks. That all makes sense to me.
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