Question

1. v=v0+at
2.x=x0+v0t+(1/2)at^2
For problem solving it is useful to eliminate a by substituting for a from 1 Into 2.
x=x0+(1/2)(v0+v)t
For problem solving eliminate t in 2 by substituting for t from 1.
v^2=v0^2+2a(x-x0)
I keep messing this up. For the first one I keep geting x=x0+(1/2)vt

Answer 1

1. v = v0 + at

v - v0 = at

v - v 0 = a
------
t

agree?

Answer 2

yes

Answer 3

so that would give you

x = x0 + v0t + (v - v0)t^2 / 2t

so you have \[\implies x =x_0 + v_0t + \frac{(v-v_0)t}2\]

Answer 4

then if you factor out t..
\[\implies x = x_0 + t\;(v_0 + \frac{v - v_0}2)\]
convert to similar denominators..
\[\implies x = x_0 + t\; (\frac{2V_0}2 - \frac{v-v_0}2)\]

following?

Answer 5

yeah I'm following.

Answer 6

typo... that should be \[\implies x = x_0 + t \; (\frac{2V_0}2 + \frac{v-v_0}2)\]

Answer 7

so if you combine them you get
\[\implies x = x_0 + t \; (\frac{v + v_0}2)\]
that was your question right?

Answer 8

For the second one, would it be easier to use the answer for the first one to find. v^2=v0^2+2a(x-x0)

Answer 9

what do you mean?

Answer 10

The second part is: For problem solving eliminate t in 2 by substituting for t from 1.
v^2=v0^2+2a(x-x0)

Answer 11

Just use x=x0+(1/2)(v0+v)t and t=(v-v0)/a

Answer 12

sorry i have to go now. important business call

Answer 13

but you should solve for t in

v = v_0t + at

then substitute that t into

x = x_0 + v_0 t + 1/2 at^2

that should give you the answer