- #1

Spoti112

- 9

- 2

## 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 ⇒

⇒ V

^{2}/2 = x

^{2}+ c

x=1↔V=0 ⇒ 0=1

^{2}+ c ⇒ c = -1

⇒ V=√( 2 * (x

^{2}- 1) ) ⇒ V(x=3) =

__4 m/s__

(b) i have no idea... ;(