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

In summary, there are five key equations for motion, but only two are essential: vf = vi + at and d = vit + (1/2)at2. The other three can be derived from these two. However, some people may prefer using all five equations for a better understanding of kinematics.
  • #1
harujina
77
1
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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  • #2
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.
 
  • #3
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!
 
  • #4
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
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
 
  • #6
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!
 
  • #7
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
 
  • #8
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:
 

1. How do the 5 kinematic equations relate to motion?

The 5 kinematic equations are mathematical formulas that describe the relationship between an object's position, velocity, acceleration, and time. They are used to calculate the motion of an object in a straight line.

2. What are the 5 kinematic equations?

The 5 kinematic equations are:
1. d = v0t + 1/2at2 (displacement equation)
2. v = v0 + at (velocity equation)
3. v2 = v02 + 2ad (velocity squared equation)
4. d = (v + v0)t/2 (average velocity equation)
5. d = v0t + 1/2at2 (time equation)
where d is displacement, v is velocity, a is acceleration, t is time, and v0 is initial velocity.

3. How do I know which kinematic equation to use?

The kinematic equation you use depends on the information you have and what you are trying to solve for. If you have three of the variables (displacement, velocity, acceleration, or time), you can use one of the equations to solve for the fourth variable. It is important to note that the equations only work for motion in a straight line with constant acceleration.

4. Can the kinematic equations be used for any type of motion?

No, the kinematic equations can only be used for motion in a straight line with constant acceleration. If an object is moving in a curved path or the acceleration is changing, these equations will not accurately describe its motion.

5. How can I use the kinematic equations to analyze real-world motion?

The kinematic equations can be used to analyze real-world motion by collecting data on an object's position, velocity, and acceleration over time. By plugging these values into the equations and solving for the missing variables, you can better understand and predict the motion of the object. These equations are commonly used in fields such as physics, engineering, and sports science.

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