Scalars/Vectors and Distance/Displacement

Characteristics of a Scalar Quantity Only has magnitude Requires 2 things: 1. A value 2. Appropriate units Ex. Mass: 5kg Temp: 21° C Speed: 65 mph

Characteristics of a Vector Quantity Has magnitude & direction Requires 3 things: 1. A value 2. Appropriate units 3. A direction! Ex. Acceleration: 9.8 m/s2 down Velocity: 25 mph West

More about Vectors A vector is represented on paper by an arrow 1. the length represents magnitude 2. the arrow faces the direction of motion 3. a vector can be “picked up” and moved on the paper as long as the length and direction its pointing does not change

Graphical Representation of a Vector The goal is to draw a mini version of the vectors to give you an accurate picture of the magnitude and direction. To do so, you must: Pick a scale to represent the vectors. Make it simple yet appropriate. Draw the tip of the vector as an arrow pointing in the appropriate direction. Use a ruler & protractor to draw arrows for accuracy. The angle is always measured from the horizontal or vertical.

Understanding Vector Directions To accurately draw a given vector, start at the second direction and move the given degrees to the first direction. N 30° N of E W E Start on the East origin and turn 30° to the North S

Distance Distance – the length traveled by an object Practice – What is the distance? Pattie walks 4 km North, then 3 km East Joe runs 30 m East, then runs 40 meters West Aaron jogs 4 km East, 4 km North, 4 km West, and 4km South Answers: 7 km ; 70 meters ; 16 km

Distance vs. Displacement Distance – length Displacement – distance AND direction of a movement from the starting point Distance vs. Displacement

If an object moves in a single direction, the displacement equals the distance + the direction 4 km total displacement = 4km North start here 

If an object moves in two opposing directions, the displacement is the difference between the two. total distance = 4 + 3 = 7 km 3 km 4 km Displacement can be positive or negative. A negative direction can be either the opposite of the original movement, or can follow the sign of a typical graph [North/East vs South/West] start here  total displacement = 4 km North + -3 km South = 1 km North (of original starting point)

If an object moves in two directions, a triangle will be formed If an object moves in two directions, a triangle will be formed. If the angle is 90º , use a2 + b2 = c2 to solve. Displacement – cont’d 3 km 4 km displacement start here 

If an object moves in two directions, a triangle will be formed If an object moves in two directions, a triangle will be formed. If the angle is 90º , use a2 + b2 = c2 to solve. Displacement – cont’d 3 km displacement = 42 + 32 = c2 c2 = (16) + (9) = 25 c2 = √(25) c = 5km 5 km 4 km start here 

Displacement – cont’d Displacement can be given in: units with direction example: x number of meters North 30 meters East + 40 meters West displacement = 10 meters West

Displacement – cont’d Displacement can be given in: positive or negative units [like on a graph] positive = North {up} or East {right} negative = South {down} or West {left} 30 meters east + 40 meters west = 30 meters + (-40) meters = -10 meters

Displacement Practice – What is the displacement? Pattie walks 4 km North, then 3 km East 5 km displacement Joe runs 30 m East, then runs 40 meters West 10 meters [or -10] displacement Aaron jogs 4 km East, 4 km North, 4 km West, and 4km South 0 meters displacement Displacement go to website!!!!