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

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Discussion Overview

The discussion centers around the five kinematic equations used to describe motion in physics, exploring their validity, derivation, and relevance in problem-solving. Participants examine specific equations, their forms, and the conditions under which they apply, including the implications of initial velocity and constant acceleration.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant lists five kinematic equations and questions the validity of two additional equations presented by their teacher.
  • Another participant clarifies that one of the additional equations is a specific case of a kinematic equation where initial velocity is zero.
  • Some participants assert that the equation d = (vf + vi/2)t is incorrect and suggest the correct form is d = 1/2(vi + vf)t.
  • There is a claim that only two equations are essential for deriving the others: vf = vi + at and d = vit + (1/2)at².
  • One participant expresses that having all five equations can be beneficial for understanding and learning kinematics, despite some arguing that fewer equations are necessary.
  • A later reply mentions that calculus can be used to derive the kinematic equations, indicating a preference for a more fundamental understanding of motion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the necessity of all five kinematic equations versus a reduced set. There is disagreement regarding the correctness of specific equation forms and their derivations.

Contextual Notes

Some participants express uncertainty about the derivation of equations and the conditions under which they apply, particularly regarding initial velocity and the assumptions made in different contexts.

harujina
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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?
 
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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.
 
quawa99 said:
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!
 
harujina said:
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)(vi+vf)t.

Actually, only two equations are essential:

vf = vi + at
d = vit + (1/2)at2

The others can be derived from these two.
 
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
 
jtbell said:
This one is incorrect. Either your teacher or you copied it wrong.
This is the correct version, assuming you meant (1/2)(vi+vf)t.

Actually, only two equations are essential:

vf = vi + at
d = vit + (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!
 
jtbell said:
Actually, only two equations are essential:

vf = vi + at
d = vit + (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
 
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." :biggrin:
 

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