# Particle Dynamics Problem

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

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 don't know how-to get that from the derivation. Need Help Thanks!

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?

s4orce
Integral 4s^2=4s^3/3

s4orce

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

Staff Emeritus