Speed, velocity and acceleration Physics 100 Chapter 2

speed speed = v = distance traveled elapsed time 50km v = 50km 1 hr = 50 km/hr Hawaii Kai  Haleiwa In one hour This is the average speed over 1 hour. For shorter time intervals it can be higher or lower.

Earth’s motion around the Sun r=1.5x10 11 m V = distance elapsed time = 2  r 2 x 3.14 x 1.5 x m 365 days x 24 hrs/day = 1year = 9.4 x m 8760 hrs = 9.4 x m 8.76 x10 3 hrs = 1.1x10 8 m/hr = 1.1x10 5 km/hr  70,000 mi/hr

Velocity = speed + direction r=1.5x10 11 m 6 months later speed = same different direction v velocity is a “vector”: a quantity that has both magnitude and direction Length of the arrow = speed Direction of arrow same as direction of the motion

Scalars and Vectors Simple numbers: Speed v Temperature T Number + direction Velocity v relative positions r Force F Acceleration a PSB r Campus Center

Acceleration (  changes in v) acceleration = change in velocity elapsed time a = change in v elapsed time

Change in V = 100km/hr Elapsed time = 3 sec “This baby goes from 0 to 100km/hr in only 3 seconds” a = change in v elapsed time = 100 km/hr 3 s = 33 km/hr s 10 3 m 3600 s =3.6x10 3 s = 33x10 3 m 3.6x10 3 s x s = 9.1 m/s 2

Different ways to change V v v Car speeds up v Car slows up v screech! a a

Accelerations (continued) v Car turns v In all three cases, v changes. Therefore these are all examples of accelerations a

Free Fall

5m t=0 v 0 =0 t=1s v 1 =? v avg = dist time 5m 1 s == 5m/s v avg = v 0 + v v 1 2 = v12v12 = v 1 = 2v avg = 10 m/s V 1 = 10 m/s

Free-fall acceleration acceleration = change in velocity elapsed time a = 10m/s 1s = 10 m/s 2 10m/s 1s This is called the “acceleration due to gravity” and given the special symbol: g=10m/s 2 Actually g=9.8m/s 2. But 10 m/s 2 is close enough for us. g

Free fall from greater heights V 0 = 0 t = 0s V 1 = 10m/s t = 1s 5m V 2 = 20m/s t = 2s V 3 = 30m/s t = 3s V 4 = 40m/s t = 4s 15m 25m 35m 5m 20m 45m 80m Total distance 1212 gt 2

Upward toss V 4 = 0 t = 4s V 3 = 10m/s t = 3s 5m V 2 = 20m/s t = 2s V 1 = 30m/s t = 1s V 0 = 40m/st = 0 15m 25m 35m 75m 60m 35m 0m Total height 80m gt v 0 t-

Simple rule for free fall aka: projectile motion When Earth’s gravity is the only force involved: actual height = height for no gravity – ½gt 2

Horizontal toss t = 0s t = 1s 5m t = 2s t = 3st = 4s 20m 45m 80m

upward toss t = 0s t = 1s 5m t = 2s t = 3s t = 4s 20m 45m 80m

Shoot the monkey communist dead white European male

Shoot the DWEM: Slower bullet

Very fast horizontal toss t = 0s t = 1s x= 8km 5m t = 2s x=16km t = 3s x=24km 20m 45m V=8km/s

Orbital motion is free fall

Artificial satellite

Turning car An object free to slide on the dashboard, tries to follow a straight line path