Solving Rectilinear Motion Equations - Deriving at^2+v+h

[BloodyFrozen]

I can't remember how to derive this equation...

x(fluxion)
a=acceleration

x=a

From that, how do we get->

at^2+v+h

I think it had to do with integration, but I can't seem to get it to match the above.

 

[tiny-tim]

Hi BloodyFrozen!

(try using the X² icon just above the Reply box )

I don't understand what you mean by "fluxion" or "x=a"

Try starting with dv/dt = a (and dx/dt = v). ​

 

[BloodyFrozen]

at^2+vt+h

My bad.

Anyways, I think I got it...

dv/dt = a
v(t)=at+C₁
v₀=C₁

v(t)=at+v₀
x(t)=at²+v₀t+C₂
x₀=C₂

Therefore,

x(t)=at²+v₀t+x₀

Since x₀ is the position at t=0, he can just replace it as the original height.


x(t)=at²+v₀t+h₀

Correct?

 

[tiny-tim]

x(t)=at²+v₀t+h₀

Correct?

erm …

what happened to the 1/2 ? ​

 

[BloodyFrozen]

erm …

what happened to the 1/2 ? ​

Woops my bad

1/2at²...

In one of the calculus review books, it says it's -1/2at²... Why is it that?

 

[tiny-tim]

In one of the calculus review books, it says it's -1/2at²... Why is it that?

i'll guess it's talking about something being thrown up …

so if v₀ is positive, then the acceleration is negative