How many equations for kinematics?

In summary: Therefore, the final equation reduces to:##x_\text{final}=x_\text{initial}+v_\text{initial}(t+1)\ ##
  • #1
PhysicallyAbel
26
1
This is a small question about the actual number of kinematic equations. I've seen many websites derive 4 different equations, but some only use 3.

The 4th equation that I have yet to see be put to use is xfinal=xinitial+1/2(vinitial+vfinal)(time)

Could someone explain why some do not mention this 4th equation? It is it necessary for working one dimensional motion problems?
 
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  • #2
PhysicallyAbel said:
This is a small question about the actual number of kinematic equations. I've seen many websites derive 4 different equations, but some only use 3.

The 4th equation that I have yet to see be put to use is xfinal=xinitial+1/2(vinitial+vfinal)(time)

Could someone explain why some do not mention this 4th equation? It is it necessary for working one dimensional motion problems?
This equation is just calculating the average velocity and using that to find distance traveled over an interval.

It's accurate only if the velocity is constant (v initial = v final) or if the change in velocity w.r.t. time is linear (i.e., acceleration is constant).

IOW, this equation can be derived from the other kinematic equations very easily.
 
  • #3
PhysicallyAbel said:
This is a small question about the actual number of kinematic equations. I've seen many websites derive 4 different equations, but some only use 3.

The 4th equation that I have yet to see be put to use is xfinal=xinitial+1/2(vinitial+vfinal)(time)

Could someone explain why some do not mention this 4th equation? It is it necessary for working one dimensional motion problems?
Most formulations involve five variables (omitting initial displacement). Since any three values are sufficient to deduce the remaining two, there are in principle five equations, each omitting one variable. Read more in section 7 of
https://www.physicsforums.com/insights/frequently-made-errors-mechanics-kinematics/
 
  • #4
PhysicallyAbel said:
The 4th equation that I have yet to see be put to use is xfinal=xinitial+1/2(vinitial+vfinal)(time)
Let's simplify your equation just a little, and write it as distance moved, x = ½ (vi + vf)t

How to get that using equations you already know?

Start with x = vit + ½at2

Remember, for motion under constant acceleration, the acceleration is given as
a = (vf - vi)/t

Now, your exercise is to substitute this expression for 'a' into the preceding equation for x, and simplify to get the equation at the top.
 
  • #5
Actually, average velocity is defined as ##\displaystyle \ v_\text{average} = \frac{\text{displacement}}{\text{elapsed time}}=\frac{x_\text{final}-x_\text{initial}}{t} \ .##

Solving for xfinal gives :

##\displaystyle x_\text{final}=x_\text{initial} + (v_\text{average})\cdot t\ ##

As pointed out above, if acceleration is constant, then the following is also true.

##\displaystyle v_\text{average} =\frac{v_\text{initial}+v_\text{final}}{2}\ ##
 
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FAQ: How many equations for kinematics?

1. How many equations are there in kinematics?

There are four equations in kinematics, known as the kinematic equations. These equations describe the relationships between displacement, velocity, acceleration, and time.

2. Do I need all four kinematic equations to solve a problem?

No, you do not need all four equations to solve a kinematics problem. Depending on the given information, you may only need one or two equations to find the solution.

3. What are the variables in the kinematic equations?

The variables in the kinematic equations are displacement (Δx), initial velocity (v0), final velocity (v), acceleration (a), and time (t).

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

Yes, the kinematic equations are applicable to any type of motion, as long as the motion is along a straight line and the acceleration is constant.

5. How do I know which kinematic equation to use in a problem?

You can determine which kinematic equation to use by identifying which variables are known and which variable you are trying to solve for. Then, you can choose the equation that contains those variables.

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