- #1
yoleven
- 78
- 1
Homework Statement
A particle is moving along a straight line such that its acceleration is defined as a=(-2v)m/s^2.
If v=20 m/s when s=0 and t=0, determine the particle's velocity as a function of position and the distance the particle moves before it stops.
The answer is v=(20-2s)m/s ; s=10m
Homework Equations
a=[tex]\frac{dv}{dt}[/tex]
a=[tex]\frac{dv}{ds}[/tex]*[tex]\frac{ds}{dt}[/tex] which becomes...
ads=vdv
The Attempt at a Solution
given: a=(-2v) m/s
v=20 m/s
t=0
s=0
solution attempt:
a=[tex]\frac{dv}{dt}[/tex]
-2v*dt=dv
dt=-[tex]\frac{dv}{-2v}[/tex]
[tex]\int dt[/tex] = [tex]\int\frac{dv}{-2v}[/tex]
That's as far as I can get. If I evaluate the left hand side from 0 to t, I get t.
If I evaluate the left, I get messed up. If I pull out the -[tex]\frac{1}{2}[/tex],
I am left with [tex]\frac{1}{v}[/tex]. I think the integral of that is ln v.
I need some direction on this one please.