Derivation of the Kinematic Equations - Jpsaos.com

taupeselectionΜηχανική

14 Νοε 2013 (πριν από 3 χρόνια και 8 μήνες)

76 εμφανίσεις

Physics 1





Robak


K
K
i
i
n
n
e
e
m
m
a
a
t
t
i
i
c
c


E
E
q
q
u
u
a
a
t
t
i
i
o
o
n
n
s
s


(
Study

of
HOW

objects move
)


EQ 1:

1
2
t
t
v
v
t
v
a
i
f










EQ. 2 is derived from EQ. 1:



t
v
v
a
i
f






i
f
v
v
at




EQ 2:

at
v
v
i
f





From a v
-
t graph, we found displac
ement (total area under the curve). The total area is
the sum of the area of the rectangle, v
i
t, and the area of the triangle, ½
(
v
f



v
i
)
t.


Total area is the displacement:



t
v
v
t
v
d
i
f
i
)
(
2
1







EQ 3:

t
v
v
d
i
f
)
(
2
1





To obtain EQ. 4, substitute EQ. 2 into EQ. 3:



EQ. 3:
t
v
v
d
i
f
)
(
2
1




and we know from EQ. 2 that
at
v
v
i
f


, so



t
at
v
v
d
i
i
)]
(
[(
2
1





t
at
v
d
i
)]
2
[(
2
1



which finally yields


Physics 1





Robak


EQ. 4:
2
2
1
at
t
v
d
i




To obtain EQ. 5, multiply EQ. 1 by EQ. 3:


EQ 1:


1
2
t
t
v
v
t
v
a
i
f










and


EQ. 3:
t
v
v
d
i
f
)
(
2
1





t
v
v
t
v
v
ad
i
f
i
f
)
)(
2
1
)(
(







)
)(
2
1
)(
(
i
f
i
f
v
v
v
v
ad








)
)(
(
2
i
f
i
f
v
v
v
v
ad








2
2
2
i
f
v
v
ad








EQ. 5:
ad
v
v
i
f
2
2
2