Objectives  Define coordinate systems for motion problems.  Recognize that the chosen coordinate system affects the sign of objects’ positions.  Define displacement.  Determine a time interval.  Use a motion diagram to answer questions about an object’s position or displacement.

COORDINATE SYSTEM Coordinate System - tells you the location of the zero point of the variable you are studying and the direction in which the values of the variable increase. Origin - is the point at which both variables have the value zero. You can indicate how far away an object is from the origin at a particular time on the simplified motion diagram by drawing an arrow from the origin to the point representing the object, as shown in figure. 2.6 Position - is the separation between an object and the origin. It can be positive or negative. It is a vector quantity. Distance – describes how far an object is from its origin. It is a scalar quantity.

VECTORS AND SCALARS Magnitude – a measure of size. Vectors – quantities that have both magnitude (size) and direction. Scalars – quantities that have only magnitude (size). To add vectors graphically, the length of a vector should be proportional to the magnitude of the quantity being represented. So it is important to decide on the scale of your drawings. The important thing is to choose a scale that produces a diagram of reasonable size with a vector that is about 5–10 cm long. Resultant – the vector that represents the sum of the other vectors. The resultant always points from the Tail of the First vector to the tip or head of the Last vector.

TIME INTERVALS AND DISPLACEMENT Time Interval – the difference between 2 times. It is equal to the final time minus the intial time. We will use the equation Δt = t f – t i Displacement – a change in position having both magnitude and direction. It is equal to the final position minus the initial position. It is a vector quantity. We will use the equation Δd = d f – d i How do you subtract vectors? Reverse the subtracted Vector and Add. To completely describe an object’s displacement, you must indicate the distance it traveled and the direction it moved. Thus displacement is not the same as distance, it is Distance and Direction.

QUESTION 1 Differentiate between scalar and vector quantities. Quantities that have both magnitude and direction are called vectors, and can be represented by arrows. Quantities that are just numbers without any direction, such as time, are called scalars.

QUESTION 2 What is displacement? Displacement – a change in position having both magnitude and direction.