2D  1
Motion in 2D
Velocity and acceleration are vectors
.
They can have any
direction.
When we are considering
motion in the xy plane, these vectors can point anywhere in the plane. A common example of
motion in 2D is.
..
Projectile motion
Consider a projectile fired from a cannon, with an initial velocity
0
v
G
with a direction of
θ
above
the horizontal.
y
0x
0
0y
0
vv
c
o
s
s
i
n
=
θ
=
θ
Acceleration is a vector, and can have any direction.
But in the special case of acceleration due
solely
to
gravity
, the acceleration is always straight
down
.
Review of 1D motion:
vx
a,
v,
tt
∆∆
==
special case: a = constant
From these 3 equations (above), we can derive
(a)
o
vv a
=+
t
o
)
(b)
2
oo
xx v
t(
1
/
2
)
a
t
=+ +
(c)
22
o
vv2
a
(
x
x
−
(d)
o
v
2
+
=
x
o
, v
o
= initial position, initial velocity
x, v = position, velocity at time t
y
x
a
x
= 0
a
y
= –g
a
v
o
x
v
x
θ
v
y
10/16/2006
©
University of Colorado at Boulder
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Suppose that a = 0 .
Then
0
x
v
v
constant
t
∆
== =
∆
⇒
0
00
0
xx
v,
v
t
x
x
,
x
x
t
−
==
−
=
0
0
v
t
+
2
1
2
position if a = constant
how much more (a > 0)
or less (a < 0) distance you
go if a
0
xxv
t
a
t
≠
=+
+
±²³²´
±³´
End of 1D motion review.
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 Fall '09
 Cech
 Chemistry, General Relativity, Velocity, Bullet, ∆t

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