Four Important Kinematic Equations

doutfanaticalMechanics

Nov 14, 2013 (3 years and 7 months ago)

54 views

Four Important Kinematic Equations


Condition


One dimensional motion with constant
acceleration


The Equations


v =
at

+ v
o




x

= ½

at
2

+ v
o
t



v
2
= v
o
2

+ 2a

x




x

= ½

(v
o
+
v)t


Velocity Vs. Time Graph


v

t

Write the equations for the following


Gradient = Slope =



Total area under the graph =


Gradient = Acceleration = a = (v


v
0
)/t



By rearranging this equation;


We get:


v = at +v
0

-----------------------

1



Area under the graph:


Displacement =
Δ

x = ½
(v
-
v
0
)t

+ v
0
t


(v
-
v
0
) = at


Therefore:
-

Δ

x = ½ at
2

+ v
0
t
--------

2


(v + v
0
)/2 = average velocity =
Δ

x / t


We get:



Δ

x = ½
(v
o
+
v)t
-------

3


From equation 1: t = (v


v
0
)/a


By substituting this to equation 3,


we get:



Δ

x = ½

(v
0

+ v) .

(v


v
0
)/a


By solving the above equation we get:


v
2

= v
0
2

+ 2a
Δ
x
---------

3