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Rectilinear Motion Question

Hey, ive been trying this question for ages and cant seem to get the answer at all:

In rectilinear motion, the acceleration of a particle is given by the equation:

a = vx

where v,x are the corresponding speed and positions.

If at t=0, the speed is 2m/s, and the position of the particle is x=1m, determine the particles speed when its position is x=5m.

(Ans: v=14m/s)
Original post by tomathon1
Hey, ive been trying this question for ages and cant seem to get the answer at all:

In rectilinear motion, the acceleration of a particle is given by the equation:

a = vx

where v,x are the corresponding speed and positions.

If at t=0, the speed is 2m/s, and the position of the particle is x=1m, determine the particles speed when its position is x=5m.

(Ans: v=14m/s)



You need to manipulate the equation.

a = vx

a = dv/dt and v = dx/dt so this gives

dv/dt = (dx/dt)x

You then say
dv/dt = (dv/dx) (dx/dt)

which gives

(dv/dx)(dx/dt) = (dx/dt) x

dx/dt cancels leaving

dv/dx = x

This is now a fairly simple integral.
Can you do the rest to get v in terms of x and then the solution?

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