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August 8th, 2018, 04:17 AM  #1 
Member Joined: Oct 2015 From: Greece Posts: 81 Thanks: 6  Motion Equations: Velocity Eliminate time?
I'm reading a Physics book and currently I'm in the Motion chapter. This chapter shows how you can calculate the motion equations. Below I'm going to give you a photo of what I did so far and inside a red rectangle you can see the equation which I can't calculate. The problem is to eliminate the time quantity for velocity's equation. I tried solving a second degree equation in order to find t and replace it into the velocity's equation, but I just could not solve it: Last edited by skipjack; August 8th, 2018 at 08:55 AM. 
August 8th, 2018, 04:41 AM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,715 Thanks: 597 Math Focus: Yet to find out. 
Why not solve the first degree equation for $t$ instead?

August 8th, 2018, 04:53 AM  #3 
Member Joined: Oct 2015 From: Greece Posts: 81 Thanks: 6  LoL I'm stupid, forget about this thread Why do I always think of the hard way first? And then getting so absorbed by it that I can't see there is a simpler way... Last edited by skipjack; August 8th, 2018 at 08:55 AM. 
August 8th, 2018, 04:56 AM  #4 
Member Joined: Oct 2015 From: Greece Posts: 81 Thanks: 6 
By the way just from curiosity, is there a way to find time by solving a second degree equation and taking all the 3 possibilities from the distinctive (<0, =0, >0)? Or it's impossible? If it's possible, I would like to see a solution. Last edited by skipjack; August 8th, 2018 at 08:56 AM. 
August 8th, 2018, 05:06 AM  #5 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,715 Thanks: 597 Math Focus: Yet to find out. 
Yes a good exercise. You may actually find more insight into what the variables describe

August 8th, 2018, 06:01 AM  #6 
Member Joined: Oct 2015 From: Greece Posts: 81 Thanks: 6 
I did it!!! Can you take a look and answer my comments (inside the images)??? First Page: https://image.ibb.co/bRe6Dz/first.jpg Second Page: https://image.ibb.co/iD3Ytz/second.jpg Third Page: https://image.ibb.co/jX07Le/third.jpg Last edited by babaliaris; August 8th, 2018 at 06:04 AM. 
August 8th, 2018, 01:39 PM  #7 
Math Team Joined: Jul 2011 From: Texas Posts: 2,770 Thanks: 1424 
$v_f = v_0 + at \implies t = \dfrac{v_fv_0}{a}$ $\Delta x = v_0 \cdot t + \dfrac{1}{2}at^2$ substitute for $t$ ... $\Delta x = v_0 \left(\dfrac{v_fv_0}{a}\right) + \dfrac{a}{2} \left(\dfrac{v_fv_0}{a}\right)^2$ $\Delta x = \dfrac{v_0v_f  v_0^2}{a} + \dfrac{a(v_f^2  2v_fv_0 + v_0^2)}{2a^2}$ $\Delta x = \dfrac{2v_0v_f  2v_0^2}{2a} + \dfrac{v_f^2  2v_fv_0 + v_0^2}{2a}$ $\Delta x = \dfrac{2v_0v_f  2v_0^2+v_f^2  2v_fv_0 + v_0^2}{2a}$ $2a \Delta x = v_f^2v_0^2 \implies v_f^2 = v_0^2 + 2a \Delta x$ 

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eliminate, equations, motion, time, velocity 
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