 Physics Help Forum A body starts from origin with initial velocity U and retardation KV^3...?
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 Kinematics and Dynamics Kinematics and Dynamics Physics Help Forum Aug 28th 2008, 08:22 AM #1 Junior Member   Join Date: Aug 2008 Posts: 10 A body starts from origin with initial velocity U and retardation KV^3...? A body starts from origin with initial velocity U and retardation KV^3 where V is instantaneous velocity of the body. A) velocity of the body at any instant is √(2U^2Kt + 1) B) velocity of the body at any instant is U/[√(2U^2Kt + 1)] C) the x coordinates of the body at any instant is 1/UK * [√(2U^2Kt + 1) - 1] D) Magnitude of initial acceleration of the body is KU^3 More than one options may be correct. __________________ 先生   Aug 29th 2008, 06:35 AM   #2
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 Originally Posted by sensei A body starts from origin with initial velocity U and retardation KV^3 where V is instantaneous velocity of the body. A) velocity of the body at any instant is √(2U^2Kt + 1) B) velocity of the body at any instant is U/[√(2U^2Kt + 1)] C) the x coordinates of the body at any instant is 1/UK * [√(2U^2Kt + 1) - 1] D) Magnitude of initial acceleration of the body is KU^3 More than one options may be correct.
$\displaystyle a = -kv^3$

(which means that option D is correct)

$\displaystyle \Rightarrow \frac{dv}{dt} = -kv^3 \Rightarrow \frac{dt}{dv} = -\frac{1}{kv^3}$ where v = U when t = 0

$\displaystyle \Rightarrow t = \frac{1}{2kv^2} + C$.

Substitute v = U when t = 0: $\displaystyle C = -\frac{1}{2kU^2}$

$\displaystyle \Rightarrow t = \frac{1}{2kv^2} - \frac{1}{2kU^2} = \frac{1}{2k} \left( \frac{1}{v^2} - \frac{1}{U^2} \right)$.

Solve for v as a function of t. You get option B.

To check option C you could differentiate it and see if you get option B ....  Tags body, initial, kv3, origin, retardation, starts, velocity Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post randomuser88 Kinematics and Dynamics 5 Jul 23rd 2013 04:58 AM njuice8 Kinematics and Dynamics 0 Jan 21st 2013 08:07 PM 10hakinn Kinematics and Dynamics 1 Jan 8th 2010 06:54 AM Adrian Kinematics and Dynamics 4 Nov 16th 2009 02:50 AM pro222 Kinematics and Dynamics 5 Nov 7th 2009 10:51 PM