Two-Dimensional Motion and
Vectors
Introduction to Vectors
Scalars and Vectors
Every physical quantity can be described
as a vector or a scalar
– Scalar – a physical quantity that has only
magnitude, but no direction
Speed, distance
– Vector – a physical quantity that has both
magnitude and direction
Velocity, displacement
Scalars and Vectors
The book uses bold to represent vectors
and italics to represent scalars
Can also use directional arrows to denote
vectors
v
Vector Diagrams
Use arrows to show direction
– Length of arrow shows relative strength of
vector
Long arrow has greater magnitude than short
arrow
Vector Addition
Can only add vectors with the same units
and that describe similar quantities
– Cannot add displacement and velocity vectors
Resultant – a vector representing the sum
of two or more vectors
Triangle Method of Addition of
Vectors
Add vectors by drawing a to-scale diagram
Measure the straight line distance from the
tail of the initial vector to the head of the
final vector
Multiply by the scale
Use a protractor to determine the direction
of the resultant
Vector Addition
Vectors can be moved parallel to
themselves in a diagram
– Must remain pointing in the same direction
Vectors can be added in any order
– Total displacement remains the same
To subtract vectors – add the opposite
– A vector plus its opposite results in zero
Vector Addition
Vector Multiplication and Division
Multiplying and dividing vectors by scalars
results in vectors
– A cab driver is told to drive twice as fast
Original velocity vcab is multiplied by scalar number
2
– Result is 2vcab
– Twice as fast in opposite direction would be -2vcab