def of average velocity = t^-1 (x - x0)
(average velocity = t^-1(x-x0))t=(avearge velocity)t + x0= x - x0 + x0 = x = (average velocity)t + x0
x = (average velocity)t + x0
def of average velocity were costant acceleration is assumed = 2^-1(v0 + v)
plug into
x = (average velocity)t + x0
x = 2^-1(v0 + v)t + x0
def of acceleration = t^-1(v-v0)
(a=t^-1(v-v0))t=(at=(v-v0))a^-1 = t = a^-1(v-v0)
t = a^-1(v-v0)
plug into x = 2^-1(v0 + v)t + x0
x = 2^-1(v0 + v)a^-1(v-v0) + x0
solve for v^2
x = 2^-1(v0 + v)a^-1(v-v0) + x0
simplfy
x = (a2)^-1(v^2 -v0^2)+ x0
OK so far
(x = (a2)^-1(v^2 -v0^2)+ x0)2a
(2a)x = (v^2-v0^2) + x0 the last term should be xo*2a ng
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why i thought you had to subtract Xo from both sides???
please help me understand
It seems like you are trying to understand a problem involving the equation for average velocity and acceleration. Let's go through the steps and clarify some of the confusion.
First, let's review the given equations:
1. Average velocity equation: v_avg = t^(-1)(x - x0)
2. Equation assuming constant acceleration: v_avg = 2^(-1)(v0 + v)
3. Acceleration equation: a = t^(-1)(v - v0)
Now, you want to derive an equation involving position (x) using these equations. Let's break it down step by step:
1. Start with the equation x = v_avg * t + x0.
This equation represents the position (x) as the product of average velocity (v_avg) and time (t), plus the initial position (x0).
2. Substitute the equation for average velocity:
x = (t^(-1)(x - x0)) * t + x0.
3. Simplify the equation:
x = x - x0 + x0.
The x0 terms cancel out, leaving x = x.
At this point, you've just proved that x = x, which is not particularly informative or helpful.
Now, let's address your question about why you thought you had to subtract x0 from both sides. In the context of the equation you were working with (x = (v0 + v)a^(-1)(v - v0) + x0), it seems like you were trying to isolate the position term (x). However, subtracting x0 from both sides would not be appropriate in this case.
To solve for v^2, you need to follow a different approach. Let's continue from the point where you left off:
1. Starting with x = (a^2)^(-1)(v^2 - v0^2) + x0.
2. Multiply both sides by 2a:
(2a)x = v^2 - v0^2 + x0.
Now, if you're trying to isolate v^2, you need to move the other terms to the other side of the equation. Let's do that:
(2a)x - x0 = v^2 - v0^2.
The expression on the left-hand side, (2a)x - x0, does not simplify further. So, this is the equation relating v^2 to other variables.
Remember, each step in solving a problem should have a clear purpose and logic. Sometimes, equations can be tricky and require careful rearrangement to obtain the desired solution.