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February 2nd, 2015, 10:56 AM   #1
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A mechanics problem I'm a bit confused about.

I have a question that states that a varying force of magnitude 40-20t N is applied to a mass of 10kg...

Therefore I say by F = ma, that a = 4-2t - right?

It then says that the mass is moving forward with velocity 5 meters per second through the origin when t = 0. I'm supposed to find s(t) including the constant...

Therefore I integrate acceleration to get v = 4t - t^2 + c where c obviously equals 5 based on the velocity at t = 0. I then integrate that to find the s(t) and get s = 2t - (1/3)t^3 + 5t + d, right? The issue is, I don't know how to find the value of d?


The last part of the question is really confusing. It says I am supposed to find the furthest distance in the positive direction from the origin... I have no idea how to answer that.
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February 2nd, 2015, 11:54 AM   #2
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Quote:
s = 2t - (1/3)t^3 + 5t + d
The first term is $2t^2$, otherwise you are fine.

It says the mass is moving forward with velocity 5 meters per second through the origin when t = 0 so that means that $s(0) = 0$ i.e. the mass is at the origin at $t=0$.

Finding when the mass is furthest from the origin is about finding the maximum value of $s(t)$. This occurs at a point when $s'(t) =v(t)= 0$ and $s''(t) = a(t) \lt 0$.
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February 2nd, 2015, 01:10 PM   #3
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Quote:
Originally Posted by v8archie View Post
The first term is $2t^2$, otherwise you are fine.

It says the mass is moving forward with velocity 5 meters per second through the origin when t = 0 so that means that $s(0) = 0$ i.e. the mass is at the origin at $t=0$.

Finding when the mass is furthest from the origin is about finding the maximum value of $s(t)$. This occurs at a point when $s'(t) =v(t)= 0$ and $s''(t) = a(t) \lt 0$.
I'm sorry, I was certain I'd typed that. On the bright side, I obviously had it written correctly so it wasn't causing me any problems. Therefore d = 0 i.e. there is no constant, right? I can't believe I didn't realise that when it said maximum value....
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