Questions that could save my final grade! Please help!?

Question

These are the questions that I was wondering if you could help me out on:
)Ex1)Derive formula for linear accelerated motion:
xfinal = (xintial) + (vinitial)t + 1/2at^2
2)Derive formula for circular motion:
a=v^2/r
3)Show that energy conservation is independent of the shape of the surface.
Consider an incline and prove for arbitrary shape. Consider conserved forces.

Any insight you could offer me would be greatly appreciated.
Thanks!

Answer 1

Forget about it!
Okay, okay I'll help.

1. Do you know calculus? if you do it is simple

Give acceleration a
We know that change of velocity with respect to time is dv(t)/dt=a so
dv=a dt integrating we have

v=at + v0
similarly

ds/dt=v=at + v0
ds=(at + v0)t integrating again and
s=(1/2)at^2 + v0t +s0

2. Look up http://en.wikipedia.org/wiki/Uniform_circular_motion
They have done a good job on the derivation of the equations of centripetal acceleration.

3. Consider an incline of angle A. If the equations are independent t of the angle you are 'home free'.

Pe=Ke in this case Pe=mgh
Ke=(1/2)mV^2
V= at
t=sqrt(2S/a)
a=F/m
F=mgsin(A) and sin(A)= h/S then

a=mg(h/S)/m=gh/S
t=sqrt(2S/(gh/S))=sqrt(2S^2/gh)
finally
Ke=(1/2)m(at)^2
Ke=(1/2)m(gh/S sqrt(2S^2/gh)^2
Ke=(1/2)m(gh/S)^2 2S^2/gh
Ke=m(gh/S)^2 S^2/gh
Ke=m(gh)^2 S^2/ S^2=mgh
Ke=Pe
So Ke, at the end of the path S, is independent of the path S and is equal to the initial potential energy. This is it!

I hope your final grade is saved!