- #1

LouisL

- 13

- 8

ds/dt= v which becomes ds=v dt, where s=displacement, t =time, and v=velocity

Then we can integrate both sides of this equation, and do a little algebra, and turn the above equation into:

s − s0 = v0t + ½at2

My main question is about the integration of both sides of the equation ds=v dt: First off, is this a differential equation? If not, what type of equation is this? Going back, we first multiply dt on both sides of ds/dt= v by dt to get ds= v dt and then we integrate. 1) what math rule allows us to multiply dt to both sides of this equation? 2) What calculus rule allows us to take the integral of both sides of this equation? 3) How can I visualize that these 2 integrals as being equal? 3) Would a one year college Calculus class be enough to understand this? I took 1 year of college Calculus but don't recall learning about this.

s

⌠

⌡ ds

s0

equals

t

⌠

⌡ (v0 + at) dt

0

Thanks for any help!