How Do You Determine a Particle's Velocity as a Function of Position?

[s4orce]

1. A particle is moving along a straight line such that its acceleration is defined as a=(4s^2)m/s^2, where s is in meters. If v=-100m/s when s=10m and t=0, determine the particles velocity as a function of position.
2. V=ds/dt a=dv/dt
3. V=ds/dt a=dv/dt 1/dt=ads*vdv
Integral 100 to s 4s^2ds=Integral -100 to v vdv

Integral 4s^2=4s^3/3What do I do now, the answer is 16.89 ft. but I don't know how-to get that from the derivation. Need Help Thanks!

 

[cristo]

What've you done here: 1/dt=ads*vdv?

Your first equation a=4s² is a differential equation: namely $$\frac{d^2s}{dt^2}-4s^2=0$$. Do you know how to solve such an equation?

 

[s4orce]

Integral 4s^2=4s^3/3

 

[s4orce]

help me solve this please

 

[s4orce]

need help i don't know what to do

 

[teknodude]

Cristo gave you the equation, so solve the diff eq. Also the answer to the problem that you posted 16.89 ft, is not right. The question isn't asking for a numerical answer.

Another way is take the equations you have V=ds/dt a=dv/dt and eliminate dt and just integrate and do the algebra.

 

[s4orce]

can you post how you did it please

 

[s4orce]

if you got 15, for the answer that's not it also

 

[cristo]

s4orce, the question is not looking for a numerical answer; it is looking for an expression for velocity. The way I would do it, would be to solve the ODE I gave you in post 2, and then differentiate the answer wrt time.

Do you know how to solve such a differential equation?

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