PHY183-Lecture7 - Position velocity and acceleration...

August 31, 2006 Physics for Scientists&Engineers 1 1
Physics for Scientists &
Engineers 1
Engineers 1
Fall Semester 2006
Lecture 7
August 31, 2006 Physics for Scientists&Engineers 1 2
Position, velocity and acceleration vectors
! Related through derivatives and integrals
( )
( )
( )
( )
( )
x t
dx t
v t
dt
dv t
a t
dt
!
=
!
=
0
0
0
0
( ) ( ') '
( ) ( ') '
( )
t
t
x t x v t dt
v t v a t dt
a t
= +
!
= +
!
"
"
August 31, 2006 Physics for Scientists&Engineers 1 3
Summary: Five Kinematical Equations Summary: Five Kinematical Equations
! One-dimensional motion with constant acceleration :
! Can solve practically all one-dimensional problems
0
2
1
0 0 2
1
0 0 2
0 0
2 2
0 0
( )
( )
[ ( )]
( )
( ) 2 [ ( ) ]
t
t
v t v at
x t x v t at
v v v t
x t x v t
v t v a x t x
!
!
= +
= + +
= +
= +
" = "
August 31, 2006 Physics for Scientists&Engineers 1 4
Free Fall
! Particular motion with constant acceleration in 1 d
• a = - g, with g = 9 . 81 m/s 2
• Conventional notation: call vertical axis y axis
! Kinematic equations for this case
0
2
0 0
1
0 0 2
0 0
2 2
0 0
1
2
( )
( )
[ ( ) ]
( )
( ) [ ( ) ] 2
t
t
v t v t
y t y v t t
v v t v
y t y v t
v t v y t y
g
g
g
!
!
=
= +
= +
"
= +
" = "
"
"
g y
F mg mge = = !
!
! !
x
y
g
F ma
mg ma
g a
=
! =
! =
!
!
Newton’s Second law
Use those for constant
acceleration:
X -> y
a -> -g

August 31, 2006 Physics for Scientists&Engineers 1 5
Remarks on Free Fall
! All objects fall at the same rate,
because
a = -g
= constant
• Need to get rid of air resistance
effects to see this
• Experiment => calculation of g
! In space, there is almost no
gravity
• Why all objects float around
• Not net force: constant velocity,
independent of the mass
0
2
0 0
1
0 0
2
0 0
2 2
0 0
1
2
( )
( )
[ ( ) ]
( )
( ) [ ( ) ] 2
t
t
v t v t
y t y v t t
v