My Math Forum A mechanics problem I'm a bit confused about.

 Physics Physics Forum

 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
Math Team

Joined: Dec 2013
From: Colombia

Posts: 7,671
Thanks: 2651

Math Focus: Mainly analysis and algebra
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
Member

Joined: Jul 2014
From: Seattle

Posts: 96
Thanks: 2

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 Display Modes Linear 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

 Contact - Home - Forums - Cryptocurrency Forum - Top