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October 30th, 2010, 01:46 PM  #1 
Member Joined: Oct 2010 Posts: 32 Thanks: 0  velocity of a body moving along the saxis v = t^24t +3 >>
hello ! porticle motion at time t>=0 , the velocity of a body moving along the saxis v = t^24t +3 a ) Find the body acceleration each time the volicty is zero . b ) When the body moving forward ? backward ? c) when is the body's velocity increasing ? deceasing ?  the answer>>>>> [color=#0000FF]a ) v = 0 2t4 = 00 t = 2 acceleration = dv/dt = 2 b) I'm not sure for this answer : v = (2)^2 4(2) + 3 = 1 then the body moving backward c ) body's velocity is deceasing [/color] 
October 30th, 2010, 03:50 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: velocity of a body moving along the saxis v = t^24t +3
We are given a) Find the body's acceleration each time the velocity is zero. Thus, the velocity is zero at t = 1 and t = 3. b) When is the body moving forward? backward? v(0) = ()() = positive, moving forward on [0,1) v(2) = (+)() = negative, moving backward on (1,3) v(4) = (+)(+) = positive, moving forward on (3,?) c) When is the body's velocity increasing? decreasing? We equate a(t) to zero, the check the interval(s). a(t) = 2(t  2) = 0 a(t) is zero at t = 2. a(0) = negative, velocity decreasing on [0,2) a(3) = positive, velocity increasing on (2,?) 
October 30th, 2010, 07:15 PM  #3 
Member Joined: Oct 2010 Posts: 32 Thanks: 0  Re: velocity of a body moving along the saxis v = t^24t +3
Hi all the velocity is zero at t = 1 and t = 3. why you talke 3 why didny take 1 to 2 ? 
October 30th, 2010, 07:34 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: velocity of a body moving along the saxis v = t^24t +3
Well, part (a) asks what the acceleration is when the velocity is zero. Factoring the given v(t) we find Thus, the velocity is zero when t = 1 and t = 3. So we use those values for t in a(t) which we find by differentiating v(t) with respect to t, which is 2 is not a zero for v(t), but it is a zero for a(t), which tells us when the velocity changes the sign of its rate of change. Graph of velocity: Graph of acceleration: 
October 30th, 2010, 11:19 PM  #5 
Member Joined: Oct 2010 Posts: 32 Thanks: 0  Re: velocity of a body moving along the saxis v = t^24t +3
I forget how we can get (t1 ) (t3 ) = 0 helo ne in this step .

October 31st, 2010, 01:30 AM  #6 
Member Joined: Oct 2010 Posts: 32 Thanks: 0  Re: velocity of a body moving along the saxis v = t^24t +3
thanks now I understand all


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