Deriving Kinematics Equations

In summary, by solving for time in the first equation and substituting it into the second equation, the formula V2x^2=V1x^2+2ax(delta)t can be derived. It is also easier to solve the problem by removing the x-components and using the one dimensional accelerated motion formulas from grade 11, specifically V^2 - Vi^2 = 2*a*d.
  • #1
Intagral
1
0
The Problem:
Using V2x=V1x+ax(deltat)t and (delta)x=V1x(delta)t + 1/2ax(delta)t^2 derive the formula V2x^2=V1x^2+2ax(delta)t


Homework Equations


1st and 3rd x-component Kinematics Equations


The Attempt at a Solution


Ok, so I attempted to solve it, but it didn't work. I don't want the answer but could someone just push me in the right direction.
 
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  • #2
Solve the v2x = equation for time. Substitute that expression into the other equation to eliminate time. Simplify. You will find that
V2x^2=V1x^2+2ax(delta)t
will not have the delta t at the end.

By the way, much easier if you leave out all those x's. These are just the one dimensional accelerated motion formulas from grade 11:
V = Vi + at and d = Vi*t + 0.5*a*t^2
and the one you are looking for is V^2 - Vi^2 = 2*a*d
 
  • #3


Sure, no problem! It looks like you are on the right track by using the first and third x-component kinematics equations. Let's start by rearranging the first equation to solve for V2x: V2x = V1x + ax(deltat)t. Now, we can substitute this expression for V2x into the third equation, (delta)x = V1x(delta)t + 1/2ax(delta)t^2, giving us: (delta)x = (V1x + ax(deltat)t)(delta)t + 1/2ax(delta)t^2. Now, we can simplify this equation by distributing the (delta)t to both terms inside the parentheses, giving us: (delta)x = V1x(delta)t + ax(delta)t^2 + 1/2ax(delta)t^2. Combining like terms, we get: (delta)x = V1x(delta)t + 3/2ax(delta)t^2. Finally, we can rearrange this equation to solve for V1x^2, giving us: V1x^2 = (delta)x - 3/2ax(delta)t^2. Now, we can substitute this expression for V1x^2 into the original equation, V2x^2 = V1x^2 + 2ax(delta)t, giving us: V2x^2 = (delta)x - 3/2ax(delta)t^2 + 2ax(delta)t. Simplifying this equation gives us the desired result: V2x^2 = (delta)x + 1/2ax(delta)t^2. I hope this helps to guide you in the right direction!
 

1. What exactly are kinematics equations?

Kinematics equations are mathematical equations that describe the motion of an object without taking into account the causes of the motion, such as forces and energy. They involve variables such as distance, time, velocity, and acceleration, and are used to calculate the position, velocity, and acceleration of an object at a given time.

2. Why are kinematics equations important?

Kinematics equations are important because they allow us to analyze and understand the motion of objects in a more quantitative way. They also help us make predictions about the position, velocity, and acceleration of an object at any given time, which can be useful in various fields of science and engineering.

3. How are kinematics equations derived?

Kinematics equations are derived using calculus and the principles of motion, such as position, velocity, and acceleration. The equations are based on the relationships between these variables and are obtained through mathematical calculations and manipulation.

4. What are the basic kinematics equations?

The most commonly used kinematics equations are the equations for constant acceleration, which include the equations for position, velocity, and acceleration. These equations are:

- Position (x) = x0 + v0t + 1/2at2

- Velocity (v) = v0 + at

- Acceleration (a) = (v - v0)/t

5. Can kinematics equations be used for any type of motion?

Kinematics equations can be used for any type of motion, as long as the acceleration is constant. This means that the equations can be applied to objects moving in a straight line with a constant speed, as well as objects moving in a curved path with a constant acceleration. However, they cannot be used for objects with varying acceleration, such as those under the influence of changing forces.

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