This document discusses key concepts in kinematics including displacement, velocity, acceleration, and how they relate to each other and can be represented graphically. It defines displacement as a change in position, velocity as the rate of change of position, and explains how to calculate displacement using velocity and time. It also describes different types of graphs used in kinematics such as velocity vs. time graphs, acceleration vs. time graphs, and position vs. time graphs and how to interpret features of these graphs like slope, area under curves, and curvature to determine properties of an object's motion like velocity and acceleration.

1. Displacement and Velocity
(velocity v.s. time and acceleration v.s. time curves)

2. Displacement is the change in position
of an object given:
 Note: SI unit for
displacement is the
meter (m). If units other
than meter are used, you
may need to convert
them into meters to
complete the
calculation.

3. Velocity is a vector quantity that refers to
"the rate at which an object changes its
position."
 Note: SI unit of velocity
is meters per second
(m/s)

4. To compute displacement using velocity
and time
 The relationship
between displacement,
velocity, and time is
given in the formula
used in solving velocity

5. Velocity v.s. time graphs
 Velocity versus time graph is the record of an object's velocity. In these graphs,
higher means faster not farther.
 When the curve on a velocity vs time graph is straight but not horizontal, the
velocity is changing.
 The graph with the steepest slope experiences the fastest change in velocity.
 On a velocity vs time graph:
 slope equals acceleration.
 the "y" intercept equals the initial velocity.
 when two curves coincide, the two objects have the same velocity at that time.
Displacement on velocity v.s. time
graphs
 For velocity versus time graphs, the area bound by the line and the axes
represents the displacement.

6. The acceleration versus time graph of any
object traveling with a constant velocity is
the same.
 When acceleration is constant, the acceleration-time curve is a horizontal line.
 On an acceleration vs time graph:
 slope is meaningless.
 the "y" intercept equals the initial acceleration.
 when two curves coincide, the two objects have the same acceleration at
that time.
 an object undergoing constant acceleration traces a horizontal line.
 zero slope implies motion with constant acceleration.
Velocity on acceleration versus time graphs
 The area under an acceleration versus time graph represents the change in
velocity.

7. Position v.s. Time Graph
 Position-time graphs are the most basic form of graphs in kinematics, which allow
us to describe the motion of an object with respect to position and time.
 The y-axis of these graphs represent the distance travelled by the object, and the
x-axis represents the time.

8. Characteristics of Position v.s. Time
Graph
 The specific features of the motion of objects are demonstrated by the
shape and the slope of the lines on a position versus time graph.
 The vertical axis represents the position of the object.
 The slope of a position graph represents the velocity of the object. So the
value of the slope at a particular time represents the velocity of the
object at that instant.
 The curvature in a graph means the object is accelerating, changing
velocity/slope.
 If the curvature of the position graph looks like an upside down bowl, the
acceleration will be negative.
 If the curvature looks like a right side up bowl, the acceleration will be
positive

9. Acceleration on velocity v.s. time
graph
 On a velocity versus time graph, the average acceleration is the slope of the
straight line connecting the endpoints of a curve