Distance and Displacement Chapter 11.1

How would you describe the butterfly’s motion? How fast? Toward the flower or away from it? To describe motion, you must state the direction the object is moving as well as how fast. You must also tell its location at a certain time.

Choosing a Frame of Reference How fast is the butterfly moving? Butterfly is moving on Earth Earth is moving (rotating and revolving around the sun) SO…the butterfly is moving very, very fast!! To describe motion accurately you need a frame of reference.

Frame of Reference Frame of Reference = a system of objects that are not moving with respect to each other. So, how fast is the butterfly moving? Depends on which frame of reference you use.

How Fast Are You Moving? Think of riding on a train… How fast are the passengers moving? Their motion is relative… …depends on the frame of reference you choose

How Fast Are You Moving? Relative motion = movement in relation to a frame of reference People on platform will see passengers on train speeding by When people on train look at each other, they don’t seem to be moving at all

Which Frame Should You Choose? Choosing a meaningful frame of reference allows you to describe motion in a clear and relevant manner. Riding on train… Look out window, moving fast relative to ground Walk down isle, moving slower relative to floor

Measuring Distance Distance = the length of a path between two points Helpful to express distances in units that are best suited to the motion you are studying SI Unit for distance = meter (m) Kilometer (km) = 1000 meters Centimeter (cm) = 1/100 meter

What unit should you use? Length of Mississippi River? 3780 km is easier than 3,780,000 meters Diameter of ping pong ball? 4 cm is easier than 0.04 meters

Measuring Displacement To describe an object’s position relative to a given point, you need to know how far away and in what direction the object is from that point. Displacement = the direction from the starting point and the length of a straight line from the starting point to the end point (distance = the length of the path between two points)

Vector vs Scalar Vector Scalar Magnitude AND Direction Magnitude 4 meters 4 meters to the RIGHT Distance Displacement 4 meters

Displacement Displacement is used in directions… “Walk 5 blocks” “Walk 5 blocks north from the bus stop” Roller coaster Measure path of car = distance Start to finish = displacement = 0

Combining Displacements Displacement is a vector. Vector = quantity that has magnitude and direction. Arrows are used to represent vectors. Length of arrow = magnitude 4 km 2 km

Displacement Along a Straight Line If two displacements have the SAME direction, ADD their magnitudes. Total displacement 4 km 2 km 4 km + 2 km = 6 km

Displacement Along a Straight Line If two displacements have OPPOSITE directions, SUBTRACT the magnitudes from each other. Total displacement 2 km 4 km 4 km - 2 km = 2 km

Displacement That is NOT Along Straight Line Combine by graphing. Resultant vector = vector sum of two or more vectors 3 meters a2 + b2 = c2 42 + 32 = c2 16 + 9 = c2 25 = c2 5 = c 5 meters NE is the resultant vector b a 4 meters c

KHANACADAMY video: “Introduction to Vectors and Scalars” https://www.khanacademy.org/science/physics/one-dimensional-motion/displacement-velocity-time/v/introduction-to-vectors-and-scalars