Kinematics problem with differential equations.

  • #1
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Homework Statement


Suppose the acceleration of a particle is a function of x, where a(x)=(2.0 s-2)*x.
(a) If the velocity is zero when x= 1.0 m, what is the speed when x=3.0 m?
(b) How long does it take the particle to travel from x=1.0 m to x=3.0 m.


a(x)=(2.0 s-2) * x
(a) V(x=3) = ? , V(x=1) = 0
(b) t=? (from x=1 to x=3)

Homework Equations


a=dV/dt
V=dx/dt

The Attempt at a Solution


(a) a = dV/dt = (dV/dx) * (dx/dt)= (dV/dx) * V ⇒
⇒ a = 2x = (dV/dt) * V ⇒ VdV = 2xdx ⇒ ∫VdV = ∫2xdx ⇒
⇒ V2/2 = x2 + c
x=1↔V=0 ⇒ 0=12 + c ⇒ c = -1
⇒ V=√( 2 * (x2 - 1) ) ⇒ V(x=3) = 4 m/s

(b) i have no idea... ;(
 

Answers and Replies

  • #3
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2
dx/dt = √( 2 * (x2 - 1)) → dt = dx/√(2(x2 - 1)) .... and i`m stuck with the math
if i integrate here in an interval of 1 to 3 (both sides ) , wont i lose the t in the equation ?
 
  • #4
haruspex
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an interval of 1 to 3 (both sides )
The 1 to 3 is the x range. The t range is the duration, from tx=1m=0 to t=tx=3m.
 
  • #5
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thank you very much for the help!
 

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