/sci/ - Science & Math » Thread #12451323

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Anonymous Fri 11 Dec 04:14:23 2020 No.12451323 View Reply Original Report

Quoted By: >>12451411

How do you derive the kinematic equation:

deltaX = ((Vf+Vo)/2)t

Using calculus? There are tons of videos deriving every other kinematic equation but for some reason everyone just fucking forgets this one.

Anonymous

Anonymous Fri 11 Dec 2020 04:38:49 No.12451411 Report

Quoted By: >>12451464

>>12451323
this equation assumes constant acceleration (a is just a number)
$\ddot{x}=a \\<br />\int_{t_0}^{t_f} \ddot{x} dt = \Delta v = a \Delta t \rightarrow a= \frac{\Delta v}{ \Delta t} \\<br />\int_{t_0}^{t_f} \dot{x} dt = \Delta x = \frac{1}{2} a(\Delta t)^2 = \frac{1}{2} \Delta v \Delta t$

Anonymous

Anonymous Fri 11 Dec 2020 04:52:12 No.12451464 Report

Quoted By: >>12451541

>>12451411
I don't understand what you did here. Why did you end up with deltaV when the kinematic equation says Vf *plus* Vo? deltaV would be Vf - Vo.

I don't really understand several of your other steps either. What exactly did you start with? a = dV/dt? How does deltaX = (1/2)a(deltat)^2?

Anonymous

Anonymous Fri 11 Dec 2020 05:21:50 No.12451541 Report

Quoted By: >>12451551

>>12451464
the C you get in integrals is the v_0 and the x_0

Anonymous

Anonymous Fri 11 Dec 2020 05:26:07 No.12451551 Report

Quoted By:

>>12451541
That still doesn't answer the question of how Vf - Vo turns into Vf + Vo. If someone could give a more step-by-step process for a retard like me that would be great.

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