I'm struggling on manipulating kinematics

[Rebecca Berger]

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.

 

[berkeman]

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.

 

[cnh1995]

v=v0t+at,

Shouldn't this be v=v0+at?
I believe taking square on both the sides of this equation would help.

 

[Rebecca Berger]

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)]

 

[Rebecca Berger]

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]

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

 

[vnsridhar]

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.