Mastering the 5 Kinematic Equations: An In-Depth Look at Motion Rules

[harujina]

I know that there's 5 key equations for motion which is:

d = (vf+vi/2)t
vf = vi + at
d = vit + 1/2at^2
vf^2 = vi^2 + 2ad
d = vft - 1/2at^2

Correct?
But my teacher was confusing me today and he taught us these two other equations:

d = 1/2(vi+vf)t
d = 1/2at^2

What are these? Are they just other "rules of motion" like everything else?

 

[quawa99]

The second equation 'D=1/2at^2' is one of the kinematic equations 'D=Vi+1/2at^2' where the initial velocity 'Vi' is considered to be zero.

 

[harujina]

The second equation 'D=1/2at^2' is one of the kinematic equations 'D=Vi+1/2at^2' where the initial velocity 'Vi' is considered to be zero.

oh right, i can't believe i didn't notice that! ok thank you!

 

[jtbell]

d = (vf+vi/2)t

This one is incorrect. Either your teacher or you copied it wrong.

d = 1/2(vi+vf)t

This is the correct version, assuming you meant (1/2)(v_i+v_f)t.

Actually, only two equations are essential:

v_f = v_i + at
d = v_it + (1/2)at²

The others can be derived from these two.

 

[namanjain]

5 eq

v final velocity
u initial vel.
t time
s displacement
a constant accⁿ


v= u +at
s= ut + .5at²
v²= u² +2as
s= vt - .5at²
s= .5(v+u)t

 

[namanjain]

This one is incorrect. Either your teacher or you copied it wrong.
This is the correct version, assuming you meant (1/2)(v_i+v_f)t.

Actually, only two equations are essential:

v_f = v_i + at
d = v_it + (1/2)at²

The others can be derived from these two.

but while doing numerical it is irritating to first get acceleration, so actually 5 eqⁿ
are good adding to it this gives feel to a child what he's doing
also kinematics it a beginning so one can learn these quickly as afterward formula formula formula!

 

[dauto]

Actually, only two equations are essential:

v_f = v_i + at
d = v_it + (1/2)at²

The others can be derived from these two.

You can chose any two out of the five to take as essential and derive the other three from them

 

[jtbell]

True, but I like those two because if you know calculus you can get them by integrating d²x/dt² = a twice. Of course, that means you really need to remember only one equation which basically just says "acceleration is constant."