# Derivation of the Kinematic Equations - Jpsaos.com

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14 Νοε 2013 (πριν από 4 χρόνια και 5 μήνες)

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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