How Do You Derive the Equations of Motion in Physics?

[kevinli]

Please help! Easy motion question!

Homework Statement

Please explain these steps to me. My physics teacher went too fast :(

v=a*t
d=v*t
d=(a*t)*t
d=at²
V_average=V_f/2
=1/2V_f
d=1/2V_f*t
d=1/2at²

Thank you for your help

Homework Equations

v=a*t -> d=1/2at²

The Attempt at a Solution

N/A

 

[Fazza3_uae]

Hi kevinli , welcome to PF ^^

first equation (v=a*t) is for Velocity = acceleration * time

in units = (m/s²)*(s) = (m/s) which is the SI unit for Velocity ^^


the second one (d=v*t) is for distance = velocity * time

in units = (m/s) * (s) = (m) which is also the SI unit for Distance


In this equation (d=(a*t)*t) he just substitued v with (a*t)

and he got this one (d=at2)



Here in this equation (Vaverage=Vf/2) i think he assumed Vi = 0
the initial velocity = 0 so the average Vf-Vi=Vf and divide by 2 ^^


He used the average velocity = (1/2)Vf in this equation d=v*t Instead of v

So he will get d= (1/2)Vf * t

and from first equation v=a*t

Or we can say Vf=a*t
we get

d=(1/2)at²

And finally i want to tell U that these equations will help U In free fall or projectiles
I hope i have explained what U want , & hope that u get it well now if it is what u want to know ^^

 

[Redbelly98]

Welcome to PF kevinli

Homework Statement

Please explain these steps to me. My physics teacher went too fast :(

v=a*t

What is v here? We talk about average, initial, and final velocity. Which velocity is it?

d=v*t

That should read

d = V_average*t​

d=(a*t)*t
d=at²

The above 2 equations are wrong.

V_average=V_f/2
=1/2V_f
d=1/2V_f*t
d=1/2at²

Look at these last two equations. If they are true (which they are), that implies that

V_f = ____?​