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 February 2nd, 2015, 10:56 AM #1 Member   Joined: Jul 2014 From: Seattle Posts: 96 Thanks: 2 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. 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 $s''(t) = a(t) \lt 0$. February 2nd, 2015, 01:10 PM   #3
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Quote:
 Originally Posted by v8archie 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.... Tags bit, confused, mechanics, problem Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post abdulrehmanshaah Applied Math 0 February 9th, 2014 05:16 AM mikev Algebra 1 April 14th, 2013 11:36 PM sumukid Physics 2 August 12th, 2011 12:24 AM SarahB5 Physics 2 December 12th, 2008 06:45 AM SarahB5 Applied Math 0 December 31st, 1969 04:00 PM

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