Motion A change in position relative to some reference point during a period of time.

Speed Rate at which an object moves Speed = distance/time Units: m/sec, km/hr, mi/hr. d s t

Types of Speed Instantaneous Speed – speed at a given instant. Average Speed = ∆ distance/ ∆ time. Describes speed of motion when speed is changing. Constant Speed – speed that doesn’t change.

Speed Problems What is the speed of a cyclist who travels 50 meters in 25 seconds? S = d/t 50 m/25 s 2 m/s You are in a car traveling an average speed of 60 km/hr. The total trip is 240 km. How long does the trip take? t = d/s 240 km/60 km/hr 4 hrs.

Distance -Time Graphs Time (sec) Time (sec) Time (sec) Time (sec) Distance (m) Distance (m) Time (sec) Time (sec) Distance (m) Distance (m) Time (sec) Time (sec)

Velocity Speed in a given direction. Uses: Navigation (airplanes, ships), weather, etc. Vector quantity – represented graphically by arrows ( ). Length = magnitude Arrowhead = direction

Velocity Problem If you row a boat upstream at 10 km/hr and the river has a downstream velocity of 5 km/hr, you are actually moving at what velocity? = 5 km/hr downstream 10 km/hr upstream 5 km/hr upstream

Acceleration Rate of change in velocity. Really a description of “how fast you can go in a certain amount of time”. Good acceleration is being “quick to change”.

Acceleration Examples: speeding up (+ acc.), slowing down (- acc.), or changing direction. Acc. = final velocity – original velocity/time. Units: m/sec/sec Represented by a Velocity – Time Graph

Velocity vs. Time Graphs Time (sec) Velocity (m/s) Time (sec) Velocity (m/s) Time (sec) Velocity (m/s) Time (sec) Velocity (m/s)

Acceleration Problem A car increases its speed from 60 km/hr to 80 km/hr in 4 seconds. What is the car’s acceleration? Acc = Δ velocity time 80 km/hr – 60 km/hr 4 sec. 5 km/hr/sec. 1st second – 65 km/hr 2nd second – 70 km/hr 3rd second – 75 km/hr 4th second – 80 km/hr

Rates of Motion Table Rates Definition Equation Unit Graph Speed Velocity Acceleration

Gravitational Acceleration Acceleration on an object caused by gravity.

Falling Objects Free fall – considers only gravity & neglects air resistance. All falling objects accelerate at the same rate, regardless of their masses. - 9.8 m/sec/sec or 32 ft./sec/sec. on earth. - velocity increases 9.8 m/s each second. - distance fallen – increases mathematically

Uniform Motion Equations Instantaneous speed vf = vi + at Distance fallen d = vit + ½at2 Average speed v = vi + vf 2

Objects Thrown Straight Up

Graphing Free Fall Distance (m) velocity (m) Time (sec) Time (sec)

Air Resistance on Falling Objects Air resistance noticeably alters the motion of things like falling feathers or pieces of paper. Less noticeably on more compact objects. e.g. stones, balls