Distance vs Displacement ::Overview:: Distance vs Displacement Speed and Velocity Acceleration Linear Motion Projectile Motion Intro to Physics Unit 2: Kinematics: Motion! One Dimensional Motion An Intro to: Speed, Velocity, Acceleration

This is due TODAY– please do by the end of class today! Vocab #2 This is due TODAY– please do by the end of class today!

Section 1: Distance and Displacement After this section, you should be able to: State the difference between distance and displacement Identify which is a SCALAR and which is a VECTOR and why. Solve problems with varying distances and displacements.

What is Motion? Distance: How far an object has moved Motion- any physical movement or change in position or place, relative to a reference point Movement Happens 1 kilometer Distance: How far an object has moved

What is motion? Displacement: The distance a body changes from its original position 1 meter Y axis X axis 1 2 3 4 5 6 7 What is the final displacement?

NOTE: distance (displacement) can either be expressed by “d” or “x” Distance is the length of the actual path taken by an object. Consider travel from point A to point B in diagram below: NOTE: distance (displacement) can either be expressed by “d” or “x” It’s the same thing!! Distance s is a scalar quantity (no direction): A B s = 20 m Contains magnitude only and consists of a number and a unit. examples : (20 m, 40 mi/h, 10 gal)

Displacement B x = 12 m at 20o A A vector quantity: Displacement is the straight-line separation of two points in a specified direction regardless of the actual path taken to travel between points. A B x = 12 m at 20o q A vector quantity: Contains magnitude AND direction. examples: (12 m at 300; 8 km/h North)

Distance vs Displacement For motion along x or y axis, the displacement is determined by the x or y coordinate of its final position. Example: Consider a car that travels 8 m, E then 12 m, W. Net displacement x is from the origin to the final position: y x 8 m, E x = 4 m, W x = -4 x = +8 x 12 m, W What is the distance traveled? 8+12= 20 m

The Signs of Displacement Displacement is positive (+) or negative (-) based on location from the origin. An object can have a positive or negative displacement in either the x or the y direction. (-,+) (+,+) (-,-) (+,-) The direction of motion does not matter!

The SLOPE of a Distance vs Time graph is the SPEED! Graphing: d vs t No Motion Forward Constant Speed Distance Distance Time Time The SLOPE of a Distance vs Time graph is the SPEED!

What motion is this?? Distance Distance Time Time Distance Distance

REVIEW Distance (Scalar) - the total amount traveled regardless of path taken Displacement (Vector) – the distance from the original location (straight shot)

Vector vs Scalar Scalar – has Magnitude (value) ONLY!!! Vector – has Magnitude AND Direction!!!

Vectors Vectors are denoted by an arrow. Length of Arrow : Shows magnitude Arrow Head: Shows direction Vectors are used to solve for displacement. If an object is not moving in a straight line, the Pythagorean theorem will also be helpful.

Adding Vectors Tip to Tail Method To add vectors in this fashion, you must line up the vectors HEAD TO TAIL without changing the direction or the length of each vector:

Tip to Tail The resultant vector is a vector that connects the head of the last vector to the tail of the first vector. Resultant vector: is the only one will go “head to head” and “tail to tail”

Vector Practice – Tip to Tail Remember, ALWAYS line up vectors Tip to Tail ! IF a vector is NEGATIVE, just change it to the opposite direction. The RESULTANT vector will go head to head at the end. -B A R4