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)
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... ;(