Kinematics
Kinematics is the science of describing
the motion of objects using words,
diagrams, numbers, graphs, and
equations.
Describing Motion with
Position vs. Time Graphs
Ex:car moving with a constant,
rightward (+) velocity of 10 m/s.
What would a graph for this motion look like?
Determining Velocity on a p vs.t
Graph
• The slope of a position-time graph is the
average velocity!!!!!!!!!!!
• Pick two points on the line and determine their
coordinates.
• Determine the difference in y-coordinates of
these two points (rise).
• Determine the difference in x-coordinates of
these two points (run).
• Divide the difference in y-coordinates (rise) by
the difference in x-coordinates (run).
25m-5m =20m =4m/s
5s - 0s
5s
What can you say about the
motion of the two objects
represented in these graphs?
Slow, moving right (+) Constant Velocity
Fast, moving right (+) Constant Velocity
What can you say about the
motion of the two objects
represented in the graphs?
Slow, moving left (–) Constant Velocity
Fast, moving left (–) Constant Velocity
What if the object does not travel
at a constant velocity?
• Acceleration is a vector quantity which is
defined as "the rate at which an object
changes its velocity." An object is accelerating
if it is changing its velocity
• The shape of a position vs. time graph can tell you
what kind of motion is occurring:
• Straight line = constant velocity
• Curved line = changing velocity= acceleration
Quick Time™ an d a
d eco mp res sor
ar e n eed ed to s ee this pic tur e.
QuickTime™ and a
decompressor
are needed to see this picture.
Ex. 2 A car that is moving rightward and
speeding up or accelerating in +
direction.
What would its graph look like?
• Note that the constant velocity object has a
constant slope and the accelerating object
has a non-constant slope.
QuickTime™ and a
decompressor
are needed to see this picture.
Some data collected on a
Northward moving object
Qui ckTi me™ and a
decompressor
are needed to see thi s picture.
QuickTime™ and a
decompressor
are needed to see this picture.
QuickTime™ and a
decompressor
are needed to see this picture.
The Direction of the Acceleration
Vector
• Since acceleration is a vector quantity, it has a
direction associated with it. The direction of the
acceleration vector depends on two things:
• whether the object is speeding up or slowing down
• whether the object is moving in the + or - direction
The general RULE OF THUMB is:
•
If an object is slowing down, then its
acceleration is in the opposite direction of
its motion.
Slow to fast, moving right (+), acceleration in +
direction
Fast to slow, moving right
(+) deceleration= negative
acc.
Moving left (–) Velocity; Slow to Fast,
Acceleration (-)
Leftward (-) Velocity; Fast to Slow
Acceleration (+)
Velocity vs. time graphs
velocity
velocity
Some practice with graph shapes
• 1.
Sketch a position-time graph for an object which is moving with a
constant, positive velocity.
• 2.
Sketch a position-time graph for an object which is moving with a
constant, negative velocity.
• 3.
Sketch a position-time graph for an object moving in the + dir'n and
accelerating from a low velocity to a high velocity.
• 4.
Sketch a position-time graph for an object moving in the + dir'n and
accelerating from a high velocity to a low velocity.
• 5.
Sketch a position-time graph for an object moving in the - dir'n and
accelerating from a high velocity to a low velocity.
• 6.
Sketch a position-time graph for an object moving in the - dir'n and
accelerating from a low velocity to a high velocity.
• 7.
Sketch a position-time graph for an object moving in the + dir'n with constant
speed; first a slow constant speed and then a fast constant speed.
• 8.
Sketch a position-time graph for an object moving in the + dir'n with constant
speed; first a fast constant speed and then a slow constant speed.
• 9.
Sketch a position-time graph for an object moving in the - dir'n with constant
speed; first a slow constant speed and then a fast constant speed.
• 10.
Sketch a position-time graph for an object moving in the - dir'n with constant
speed; first a fast constant speed and then a slow constant speed.
• 11.
Sketch a position-time graph for an object which moves in the + direction at a
slow constant speed and then in a - direction at a fast constant speed.
• 12.
Sketch a position-time graph for an object which moves in the + direction at a
fast constant speed and then in a - direction at a slow constant speed.
• 13. Sketch a position-time graph for an object which moves in the - direction at a slow
constant speed and then in a + direction at a fast constant speed.