1. Kinematics: Displacement and Velocity

2. Vectors and Scalars
Most measurements that you use in everyday life are called scalar quantities, or scalars.
These quantities have only a magnitude, or size.
Mass, time, and energy are scalars. The distance an object travels and also the speed at which it travels are scalar quantities.

3. Vectors and Scalars
In physics, however, you will usually describe motion in terms of vector quantities, or vectors.
In addition to magnitude, vectors include direction.
The position, displacement, velocity, and acceleration of an object are vector quantities

5. Scalar quantities Vector quantities
Quantity
Example
Distance
15 km
Displacement
15 km [45° N of E]
Speed
30 m/s
Velocity
30 m/s [S]
Time interval
10 s
Acceleration
9.81 m/s2 [down]
Mass
6 kg
Force
2400 N [30° above
horizontal]
Energy
3600 J

6. Displacement
Displacement is the vector difference of the final position and the initial position of an object.

7. Velocity
Velocity is the quotient of displacement and the time interval.

8. Kinematics: Graphical Analysis

9. Determining the slope of a linear graph
Recall:
Graph of Velocity versus Time
velocity (m/s [East])
time (seconds)

10. Determining the area under the graph
Recall: In this case, the shape of the shaded area between the line and the x-axis is a triangle.
Graph of Velocity versus Time
velocity (m/s [East])
time (seconds)

11. Determining the slope of a curved-line graph
Determine the instantaneous velocity at 7.5 s.
First, draw tangent line on graph at 7.5 s.
Then, determine the slope of the tangent line.
Graph of Position versus Time
position (metres [North])

12. Determining average velocity on curved line position-time (d-t) graph
Determine the average velocity between 7.0 and 14.0 h.
First, draw straight line between 7.0 and 14.0 h.
Then, determine the slope of the line.