I'm struggling on manipulating kinematics

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Homework Help Overview

The problem involves manipulating kinematic equations to derive an expression for velocity that does not explicitly depend on time. The relevant equations provided are X=X0+v0t+1/2at^2 and v=v0t+at.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss various manipulations of the kinematic equations, with some attempting to isolate variables or rearrange terms. Questions arise regarding the correctness of the equations used and the steps taken in the manipulations.

Discussion Status

Several participants have provided insights and suggestions for manipulating the equations. There is a mix of approaches being explored, with some participants questioning the initial assumptions and equations used. No consensus has been reached on a single method, but guidance has been offered to clarify the steps involved.

Contextual Notes

Some participants note typographical errors in the equations presented, and there is a discussion about standard notation in kinematics. The original poster's attempts are acknowledged, but there is a lack of explicit resolution regarding the correct approach.

Rebecca Berger
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Homework Statement


Given the equations X=X0+v0t+1/2at^2 and v=v0t+at, show that an expression for v that has no explicit dependence on time can be written as v=+-√v0^2+2a(X-X0)

Homework Equations

The Attempt at a Solution


I thought I would manipulate the first given equation to be X-X0/t = [1/2(v-v0)] but as I got to the end it didn't work. Please help.
 
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Rebecca Berger said:

Homework Statement


Given the equations X=X0+v0t+1/2at^2 and v=v0t+at, show that an expression for v that has no explicit dependence on time can be written as v=+-√v0^2+2a(X-X0)

Homework Equations

The Attempt at a Solution


I thought I would manipulate the first given equation to be X-X0/t = [1/2(v-v0)] but as I got to the end it didn't work. Please help.
Welcome to the PF.

Please show us in detail your work. We can try to help if you show your work to us. :smile:
 
Rebecca Berger said:
v=v0t+at,
Shouldn't this be v=v0+at?
I believe taking square on both the sides of this equation would help.
 
I took X=X0+v0t+1/2at^2 and separated v0t because v=v0+at so it can just say vt . I then subtracted X0 from both sides and divided by t on both sides. My final equation was X-X0/t=[1/2(v+v0)]
 
cnh1995 said:
Shouldn't this be v=v0+at?
I believe taking square on both the sides of this equation would help.
Yes, sorry I made a typo
 
Rebecca Berger said:
I took X=X0+v0t+1/2at^2 and separated v0t because v=v0+at so it can just say vt . I then subtracted X0 from both sides and divided by t on both sides. My final equation was X-X0/t=[1/2(v+v0)]
I manipulated the wrong equation
 
the standard notation is v=u+at and s=ut+1/2*a*t2. Express t=(v-u)/a, substitute in s eqn, simplify and you get the answer. v2-u2=2as.
 

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