8.1 Definitions:

Magnitude refers to the size of a measurement or the amount (number) you are counting.

Scalars/Scalar Quantities are quantities that describe magnitude but do not include direction. (4 km/h)

Vectors/Vector Quantities are quantities that describe magnitude and also include direction (east, 4 km/h)

Representing Vectors

To distinguish between scalars and vectors, symbols for vectors in the textbook are bolded and written with arrows above them, whereas symbols for scalars are not.

More Definitions:

Distance (d) is a scalar quantity that describes the length of a path between two points or locations.

An odometer keeps track of the distance the car has travelled.

Position () is a vector that describes a specific point relative to a reference point. Position describes an object’s location as seen by an observer from a viewpoint. You can choose any point as a reference.

An odometer does not show which direction you went. To indicate the location of your car, you would say that the car’s position is now 10 km east of your home.

Time and Time Interval:

You are already familiar with using the concept of time (t) to describe when an even occurs.

Time Interval is the difference between the initial time (when the even begins) and the final time (when the event ends)

The symbol for change in time or time interval is t.

Both time and time interval are scalar quantities.

The time interval (t) describes the duration of the event.

Calculating the Time Interval

Christina is walking Cody along a path at 1 m per second. Suppose I want to know how long it takes to walk in a straight line from a tree to the garbage. The time Christina starts is called her initial time. Use the symbol (t ) for time and assign a subscript letter “i” for “initial time” to the time Christina is at the tree (t i ). Assign t f (final time) to the time when Christina is at the garbage can.

The time interval to travel from the tree to the garbage can is:

t = t f – t i = 5 s – 2 s = 3 s

During the 3 s time interval, Christina’s position has changed. The position of an object is measured from a reference…