Physics 20 – Graphing Vectors Concept: 1. define, qualitatively and quantitatively, displacement, velocity and acceleration 2. define, operationally, and compare and contrast scalar and vector quantities 3. explain, qualitatively and quantitatively, uniform and uniformly accelerated motion when provided with written descriptions and numerical and graphical data Types of Quantities There are two types of quantities. A. Scalar A scalar quantity indicates the amount or magnitude of a value. Most numbers you have dealt with in your life are scalars. Temperature, speed, distance, mass, a cup (of flower) are all examples of a scalar quantity. Scalar quantities that we will use in this unit are • Distance • Speed • Time • Mass B. Vector A vector quantity contains a scalar quantity (magnitude) and a direction. The direction is what makes a vector unique. Saying that something is 3m to the right of you is very different from saying that it is 3m to the left. The distance (magnitude) is 3m in both cases, but the direction tells us important information. Imagine walking over a cliff 3m to the right compared to walking 3m left to a bench. Vector quantities that we will use in this unit are • Displacement (related to distance) • Velocity (related to speed) • Acceleration Examples: Scalar Vector A distance of 100 km A displacement of 100 km northwest A speed of 50 km/h A velocity of 50 km/h up. The temperature today is 20°C A skydiver accelerates at 9.0m/s2 downward Bobo the dog has a mass of 10 kg Notation Vectors are distinguished from scalars by the direction given or in variables, by an arrow place on top. i.e d – distance compared to v 
d -­‐ displacement 
v -­‐ velocity – speed compared to Representation Directions are normally defined by using the axis of a coordinate plane. up N i.e. right W E left down S When doing math on a vector quantity such as multiplying/dividing or adding/subtracting, it is useful to draw the vectors to sketch scale drawings of them. i.e. 50 km East Tail of vector Head of vector All vectors are drawn relative to a reference point, which is a point that you choose. Every thing is measured relative to it. The tail of a vector is placed on this reference point, and is drawn from there. Mathematics When multiplying/dividing or adding/subtracting vectors, the direction must be taken into account. Rule: When multiplying vectors. The size of the multiple affects the length of the vector, and the sign (positive or negative) affects the direction. If the multiple is constant the vectors direction is unchanged. If it is negative, the vector is in the exact opposite (180°) direction. i.e. 3 × 50 km East = 150 km East -­‐3 × 50 km East = 150 km West Rule: When adding vectors together the general rule is to add the tail of a vector to the head of the previous vector. The resultant is a new vector drawn from the reference point to the head of the last vector. i.e. 50 km East + 20 km West Resultant vector = 30 km East