A. Motion Motion Change in position in relation to a reference point. Reference point Motion
A. Motion Problem: How fast is the bumblebee flying? We need a frame of reference... nonmoving point from which motion is measured. What could be used as a frame of reference in the illustration above?
Example: 1. Describe the motion of the fish in the cats frame of reference. 2. Describe the motion of the cat in the fishs frame of reference. 3. Which one is really moving; the cat or the fish?
RELATIVE MOTION: Movement in relation to a frame of reference. EX: Passengers on a rollercoaster appear to onlookers on the ground to be speeding by
Yet, when the people on the roller coaster look at each other, they dont appear to be moving at all
A. Motion Consider the following scenario: You are a passenger in a car stopped at a stop sign. Out of the corner of your eye, you notice a tree on the side of the road begin to move forward. You have mistakenly set yourself as the reference point.
Choosing a meaningful frame of reference is important in clearly describing motion!
A. Motion Distance Length of a path Choose a unit with appropriate size SI unit: meter (m) Long distances = km Short lengths = cm, mm
A. Motion Displacement Distance and direction from starting point The Millenium Force roller coaster travels 6,595 ft throughout the ride (distance) Its total displacement is zero!
A. Motion Vector Has magnitude (size, length, amount) and direction. Shown as an arrow pointing in an appropriate direction (up, down, N, S, etc); length shows magnitude Vector
A. Motion Example 1: A fire truck drives 10 miles East, then turns around and drives 2 miles West. Displacement = 10 miles E Displacement = 2 miles W Sum Vector/Disp. = 8 miles E
A. Motion Example 2: The school bus travels 2 miles East, then stops to pick up students, and continues to travel an additional 3 miles East. 2 miles E 3 miles E Resultant Vector/ Total Disp. = 5 miles E
B. Speed & Velocity Speed rate of motion distance traveled per unit time v d t
B. Speed & Velocity Instantaneous Speed speed at a given instant Average Speed
B. Speed & Velocity Problem: You are driving down Olio road, look at your speedometer, and realize youre going 80 mph. A cop clocks you. Has he measured your average or instantaneous speed? Instantaneous! You werent driving 80 mph the entire trip!
B. Speed & Velocity Problem: Your family is driving to Florida for a vacation. The trip is 1200 miles long and it takes 20 hours to get there. Is 60 mph your instantaneous speed? No! You probably sped up, slowed down, stopped for gas, or stopped to eat at several instances during the trip.
B. Speed & Velocity Problem: A storm is 10 km away and is moving at a speed of 60 km/h. Should you be worried? It depends on the storms direction!
B. Speed & Velocity Velocity speed in a given direction can change even when the speed is constant!
C. Calculations 1)Your neighbor skates at a speed of 4 m/s. You can skate 100 m in 20 s. Who skates faster? GIVEN: d = 100 m t = 20 s v = ? WORK : v = d ÷ t v = (100 m) ÷ (20 s) v = 5 m/s You skate faster! v d t
C. Calculations 2)Sound travels 330 m/s. If a lightning bolt strikes the ground 1 km away from you, how long will it take for you to hear it? GIVEN: v = 330 m/s d = 1km = 1000m t = ? WORK : t = d ÷ v t = (1000 m) ÷ (330 m/s) t = 3.03 s v d t
C. Calculations 3)The slowest animal ever discovered traveled with a speed of 5.7 km/y. How far would the crab travel in 15 y? GIVEN: v = 5.7 km/y t = 15 y d = ? WORK : d = v x t d = (5.7 km/y) x (15 y) d = 85.5 km v d t
C. Calculations 4)What is the speed of the Mediterranean crab from problem #3 in meters per day? GIVEN: v = 5.7 km/y = ? m/day WORK : 5.7 km/y x (1 mi/1.6 km) x (1 y/365 days) = d =.0098 mi/day
D. Acceleration Acceleration the rate of change of velocity change in speed or direction a: acceleration v f : final velocity v i : initial velocity t: time a v f - v i t
D. Acceleration Positive acceleration speeding up Negative acceleration slowing down
D. Calculations 1)A roller coaster starts down a hill at 10 m/s. Three seconds later, its speed is 32 m/s. What is the roller coasters acceleration? GIVEN: v i = 10 m/s t = 3 s v f = 32 m/s a = ? WORK : a = ( v f - v i ) ÷ t a = (32m/s - 10m/s) ÷ (3s) a = 22 m/s ÷ 3 s a = 7.3 m/s 2 a v f - v i t
D. Calculations 2)How long will it take a car traveling 30 m/s to come to a stop if its acceleration is -3 m/s 2 ? GIVEN: t = ? v i = 30 m/s v f = 0 m/s a = -3 m/s 2 WORK : t = ( v f - v i ) ÷ a t = (0m/s-30m/s)÷(-3m/s 2 ) t = -30 m/s ÷ -3m/s 2 t = 10 s a v f - v i t
E. Graphing Motion slope = steeper slope = straight line = flat line = Distance-Time Graph A B faster speed constant speed no motion speed
E. Graphing Motion Who started out faster? A (steeper slope) Who had a constant speed? A Describe B from min. B stopped moving Find their average speeds. A = (2400m) ÷ (30min) A = 80 m/min B = (1200m) ÷ (30min) B = 40 m/min Distance-Time Graph A B
E. Graphing Motion Acceleration is indicated by a curve on a Distance-Time graph. Changing slope = changing velocity
E. Graphing Motion Speed-Time Graph slope = straight line = flat line = acceleration +ve = speeds up -ve = slows down constant accel. no accel. (constant velocity)
E. Graphing Motion Speed-Time Graph Specify the time period when the object was... slowing down 5 to 10 seconds speeding up 0 to 3 seconds moving at a constant speed 3 to 5 seconds not moving 0 & 10 seconds