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

AI Thread Summary
The discussion focuses on deriving the equation x(t) = at² + v₀t + h₀ for rectilinear motion. Participants clarify that starting with dv/dt = a and integrating leads to the velocity function v(t) = at + v₀. The position function is then derived as x(t) = at² + v₀t + h₀, where h₀ represents the initial height. A point of confusion arises regarding the presence of the 1/2 factor in the equation, with some suggesting it may relate to objects thrown upward, where acceleration is negative. Overall, the conversation emphasizes the integration process and the correct formulation of motion equations.
BloodyFrozen
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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.
 
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Hi BloodyFrozen! :smile:

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

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

Try starting with dv/dt = a (and dx/dt = v). :smile:​
 
BloodyFrozen said:
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?:smile:
 
BloodyFrozen said:
x(t)=at2+v0t+h0

Correct?:smile:

erm :biggrin: …

what happened to the 1/2 ? :rolleyes:​
 
tiny-tim said:
erm :biggrin: …

what happened to the 1/2 ? :rolleyes:​

Woops my bad

1/2at2...:wink:

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

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