# Particle Dynamics Problem

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

Integral 100 to s 4s^2ds=Integral -100 to v vdv

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

What do I do now, the answer is 16.89 ft. but I dont know how-to get that from the derivation. Need Help Thanks!

cristo
Staff Emeritus

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?

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

need help i dont know what to do

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.

can you post how you did it please

if you got 15, for the answer thats not it also

cristo
Staff Emeritus