# Mechancis 3 dynamics, Need helpWatch

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#1
hey, I have been strugling with M3 quite a bit and was wondering if anyone could help me with this question about Further dynamics, a Solution and method would be great.

A particle P of mass 1.5kg is moving in a straight line. at time ts after it passes through a fixed point O in that line the distance OP is x m and the force acting on P has a magnitude of (3 + 3e^-2x) N and acts in the direction of OP. Given that P passes through O with speed 2 ms-1 calculate the speed of P when x = 2 and when x = 5.
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14 years ago
#2
A particle P of mass 1.5kg is moving in a straight line. at time ts after it passes through a fixed point O in that line the distance OP is x m and the force acting on P has a magnitude of (3 + 3e^-2x) N and acts in the direction of OP. Given that P passes through O with speed 2 ms-1 calculate the speed of P when x = 2 and when x = 5.
m=1.5
F=3+3(e^-2x).
x=0, v=2

f=ma
3+3e^-2x = 1.5a
a = 2 + 2e^-2x
vdv/dx = 2+2(e^-2x)
INT v dv = INT 2+2(e^-2x) dx
0.5v^2 + 2x - e^-2x + C
v^2 = 4x - 2e^-2x + k.
Using the fact x=0, v=2:
4 = -2 + k
k=6
v^2 = 6 + 4x - 2e^-2x

Plug in the values for x=2 and x=5 to find v^2 and hence v.

Don't worry if M3 seems difficult at first. As you practice more it gets better.
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#3
Thanks, you are a life saver
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14 years ago
#4
No worries. I took the M2/M3 this January and it is useful to keep it in my mind for when i go to university.
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