| Acceleration is the
time-rate-of-change of velocity. The average acceleration (aav) of a body
is defined as the ration of the change in its velocity over the time elapsed in the
process, thus: |
Average
acceleration = |
change in velocity |
| time elapsed |
|
| If we start our clocks so that ti
= 0, the final time tf is the entire trip-time, which we represent simply as t.
Hence the above equation simplifies to: |
a = |
 |
|
from the above
equation we can derive: |
Vf
- Vi = at
|
|
| Uniform acceleration takes place
in the above picture. The distances traveled in equal time intervals increases. |
A body that accelerates uniformly from
Vi to Vf over a certain
straight-line distance will cover exactly the same distance in the same time traveling at
a fixed speed of Vav , average speed.
Therefore, we have the equation: |
 |
Vav = 1/2 (Vi
+ Vf)
|
|
| Hence, we arrive to the equation
of: |
d = Vit
+ Vavt |
d = Vit
+ 1/2 (Vi + Vf)t |
| Substitute in the equation we
derived before: |
Vf -
Vi = at |
We get: |
d = Vit
+ 1/2 at2 |
|
|
|
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