Kinematic Equations
*Only hold in cases of Uniform Acceleration
(1)
(2)
(3)
  
v  v  at
o
  1  
x  x  (v  v )t
2
   1
x  x  v t  at
2
o
o
2
o
o
(4)
Traditionally there is a fourth kinematic equation that relates the velocity to the
displacement and lacks the time as a variable.
Kinematic Equation #4 Activity

Velocity v 

Displaceme nt x 
Purpose:
To create graphical and mathematical
representations of the relationship
between the velocity and the
displacement for a cart moving down a
frictionless incline.

Kinematic Equation #4 Activity
 s

vm
Side-opening Parabola

x m 
Since the graph is linear
and contains (0,0)


v 2  x
 2  m2 
v 
2
 s 

slope  2a

x m 
Data Studio
Start at 20 cm.
Kinematic Equation #4 Activity
What would change if the car was started behind 0
so that it was already moving at t = 0 s?
 s
m
v

x m 
 2  m2 
v 
2
 s 

vo2
 2  2     2
v  v2oa x2axoxxvoo
(4)

slope  2a
Data Studio

x m 
Start next to the
motion detector
Proof

v

v
Solve equation (1) for time (t)
  
v  vo  at
  
v  vo  at
 
v  vo
t 
a
 
v v
o

v
o
Substitute into equation (2) thereby
eliminating the time (t) as a variable
t
t
  
v  vo  at
(1)
  1  
x  x  (v  v )t
2
(2)
   1
x  x  v t  at
2
(3)
o
o
o
o
2
 
1
v
 
    vo 
x  xo  v  vo   
2
 a 
  
   
2a  x  xo   v  vo v  vo 
Difference of Squares!
  
2 2
2a  x  xo   v  vo
2 2
  
v  vo  2a  x  xo 
(4)
Kinematic Equations
*Only hold in cases of Uniform Acceleration
(1)
(2)
(3)
(4)
  
v  v  at
o
  1  
x  x  (v  v )t
2
   1
x  x  v t  at
2
2 2
  
v  vo  2a  x  xo 
o
o
2
o
o