- #1
Rijad Hadzic
- 321
- 20
Homework Statement
http://imgur.com/a/Y8NW0
Basically we start with a function of t, which was differentiated twice, that function = [itex] F_o / m [/itex]
Fo is a constant force, and I assume m is mass though my book doesn't state that.
Homework Equations
The Attempt at a Solution
Integrating the function, I multiply m to the other side, because I assume m is mass and mass is a constant. so it shouldn't really matter.
since F_o is a force, that means it is Kg * m/s^2, divided by mass which is in kg, you get m/s^2 which is indeed acceleration, the second derivative of time.
Integrating, I get
[itex] m\int x^{''}(t) \, dt = \int F_o \, dt [/itex]
[itex] m\int x^{''}(t) \, dt = F_o(t) [/itex]
But as you see from the link I provided, the book states
[itex] m\int x^{''}(t) \, dt = F_o(t) + V_o[/itex]
First off, I don't even know what V_o is. Is it inital velocity, or is it final velocity? It would make sense for it to be final velocity since [itex] m\int x^{''}(t) \, dt [/itex] is literally velocity itself..
I was under the impression that if you integrate something with respect to time, and that function does not have a time variable, it would simply be that function times the variable t.
Why is it that they are adding V_o in this example?