Deriving Kinematics Equations

[Intagral]

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.

 

[Delphi51]

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

 

[nlightner]

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!