DESCRIBING MOTION 0 x speed distance traveledtime x

DESCRIBING MOTION 0 x speed = distance traveled/time = (x 2 – x 1)/(t 2 – t 1) = Dx/Dt

TYPICAL SPEEDS Motion Light Earth around sun Moon around Earth Jet fighter Sound in air Commercial airliner Cheetah Falcon diving Olympic 100 m dash Flying bee Walking ant Swimming sperm Cock roach v(mph) 669, 600, 000 66, 600 2300 2200 750 600 62 82 22 12 0. 03 0. 0001 v(m/s) 300, 000 29, 600 1000 980 334 267 28 37 10 5 0. 01 0. 000045 v/c 1 10 -4 3*10 -6 10 -7 3*10 -8 3*10 -11 10 -13

EXAMPLE Speed of moon around Earth v = distance/time = 2 p. R/T R = 240, 000 mi T = 27. 3 days v = (6. 28*2. 4*105)/(27. 3*24) = 2300 mph

DISTANCE-TIME GRAPH 15 10 v= x(m) s / 5 m v 5 1 2 s / m 2 = t(s) 3

SPEED-TIME GRAPH v(m/s) 5 4 Area = 15 m 3 2 1 1 t(s) 2 3

RELATIVE SPEED v. MW v. WE v. ME = v. MW + v. WE

EXAMPLE: FLEA ON DOG ON TRAIN A train travels east with a speed v. TE = 20 km/hr A dog walks down the aisle eastward with speed v. DT = 2 km/hr A flea walks rumpward on the dog’s back with speed v. FD = 0. 01 km/hr What is the speed of the flea with respect to the Earth? v. FE = v. FD + v. DT + v. TE = -0. 01 + 20 = 21. 99 km/hr

x CHANGING SPEEDS 30 20 /s m 33 v av . 1 = 10 5 10 15 t

IMPORTANT EXAMPLE: UNIFORM ACCELERATION v t a = constant acceleration = v/t (m/s 2, mi/hr 2)

HOW FAR DOES IT GO? v at t Distance equals area under speed graph regardless of its shape Area = x = ½(base)(height) = ½(t)(at) = 1/2 at 2

DISTANCE-TIME GRAPH FOR UNIFORM ACCELERATION x t

EXAMPLE: SUPERTANKER Accelerates from 0 to 40 mph in 1 hour. so a = 40 mi/hr 2 Then x = ½(40)(1) = 20 miles If it continues for 2 hours, then x = ½(40)(4) = 80 miles

HORIZONTAL & VERTICAL MOTION Aristotle Horizontal motion: v = k. F where F = applied force Vertical motion: v = k. W where W = body’s weight

TERMINAL SPEEDS Object ` Feather Snowflake BB Mouse Sky diver Cannonball Speed (m/s) 0. 4 1 9 13 60 250 Speed (mph) 0. 9 2. 2 20 29 134 560

HORIZONTAL & VERTICAL MOTION Galileo Horizontal motion: v = constant provided F = 0 Vertical motion: acceleration = constant (neglecting air friction)

SLOWING DOWN THE MOTION

BALL ON TWO RAMPS

EXAMPLE: MARBLE IN SHOEBOX x t v t a t