2.
Motion in two dimensions, including projectile motion
a)
Students should be able to add, subtract and resolve displacement and
velocity vectors, so they can:
1)
Determine components of a vector along two specified, mutually
perpendicular axes .
2) Determine the net displacement of a particle or the location of a particle relative to another .
3) Determine the change in velocity of a particle or the velocity of one particle relative to another .
b)
Students should understand the general motion of a particle in two
dimensions so that, given functions
x
(
t
) and
y
(
t
) which describe this
motion, they can determine the components, magnitude and direction of
the particle’s velocity and acceleration as functions of time .
c)
Students should understand the motion of projectiles in a uniform
gravitational field, so they can:
1)
Write down expressions for the horizontal and vertical components of
velocity and position as functions of time, and sketch or identify graphs
of these components .
2)
Use these expressions in analyzing the motion of a projectile that is
projected with an arbitrary initial velocity .
B.
Newton’s laws of motion
1.
Static equilibrium (first law)
Students should be able to analyze situations in which a particle remains at
rest, or moves with constant velocity, under the influence of several forces .
2.
Dynamics of a single particle (second law)
a)
Students should understand the relation between the force that acts on an
object and the resulting change in the object’s velocity, so they can:
1)
Calculate, for an object moving in one dimension, the velocity change
that results when a constant force
arrowrightnosp
F
acts over a specified time interval .
2)
Calculate, for an object moving in one dimension, the velocity change
that results when a force
arrowrightnosp
F t
( )
acts over a specified time interval .
3)
Determine, for an object moving in a plane whose velocity vector
undergoes a specified change over a specified time interval, the
average force that acted on the object .
b)
Students should understand how Newton’s second law,
arrowrightnosp
arrowrightnosp
arrowrightnosp
F
F
ma
net
Â
=
=
,
applies to an object subject to forces such as gravity, the pull of strings, or
contact forces, so they can:
1)
Draw a well-labeled, free-body diagram showing all real forces that act
on the object .
2)
Write down the vector equation that results from applying Newton’s
second law to the object, and take components of this equation along
appropriate axes .

18
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c)
Students should be able to analyze situations in which an object moves
with specified acceleration under the influence of one or more forces so
they can determine the magnitude and direction of the net force, or of one
of the forces that makes up the net force, such as motion up or down with
constant acceleration .

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- Fall '10
- JOSE
- Physics, mechanics, Magnetism, AP, Harlan Hanson