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Mechanics 3 Dynamics

A particle with speed 20m/s and moves in a straight line. The particle is subjected to a resistance which produce a retardation which is initially 5m/s2which increase uniformly with the distance moved, having a value of 11m/s2 when the particle has moved a distance of 12m. given that the particle has speed v m/s when it had moved a distance xm,show that while particle is in motion,


vdv/dx=-(5+0.5x)
Original post by kkandel143
A particle with speed 20m/s and moves in a straight line. The particle is subjected to a resistance which produce a retardation which is initially 5m/s2which increase uniformly with the distance moved, having a value of 11m/s2 when the particle has moved a distance of 12m. given that the particle has speed v m/s when it had moved a distance xm,show that while particle is in motion,


vdv/dx=-(5+0.5x)


Since the retardation increases uniformily with distance, it's a linear function of distance.
So, dv/dt = ax+b................(1), where a,b are constants.

You know, I presume, that acceleration, dv/dt = v dv/dx,

It's just a case of substituting in the values given into equation (1), and solve for a,b.

Note: if the retardation is 10 ms^-2 say, then acceleration is -10 ms^-2

PS: Do see the forum guidelines on posting questions - see top of forum. I'll ignore future questions done in this format.
(edited 8 years ago)
Reply 2
Can u be more clear?? Because it doesn't addup when u plug in numbers.


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Original post by kkandel143
Can u be more clear?? Because it doesn't addup when u plug in numbers.


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What do you get then?
Reply 4
I get ur approach for solution using linear formula. But it doesn't add up when u put number in


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Original post by kkandel143
I get ur approach for solution using linear formula. But it doesn't add up when u put number in


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Saying it doesn't add up, is really helpful. Post some working.
Original post by kkandel143
...


Acceleration = ax+b.

When x is zero acceleration is -5, so

-5 = 0x+b, so b= -5.

Our equation is now

Acceleration = ax -5.

When x is 12, acceleration is -11. Now sub those in and work out a.
Reply 8
thank you very much...:smile:

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