Describing How Things Move MOTION Describing How Things Move

Motion Also called Kinematics Measured as a change in position Distances can be positive or negative Depends on the “frame of reference”

Frame of Reference Described by the observer Compares speeds and angles to the observer’s surroundings Explains the 75mph fly

Speed How rapidly an object changes location Described in units of distance divided by units of time Miles per hour Kilometers per hour Centimeters per month

Speed Formula d distance V speed = t time d distance V speed t time

What is the speed of a runner that travels 250m in 50min.? 5 m/min. 0.2 m/min. 12,500 m/min.

How long does a trip of 3000 km take if you travel at 110 km/hr.?

How far will a car traveling at 70km/hr. go in 2 hours?

Average human walking speed is 5 km/hr Average human walking speed is 5 km/hr. How far can you walk in two hours? 10 km 10 km/hr. 10 hr. 10 km•hr. None of the above

What is the speed of a bike that travels 12 km in 30 min.? 360 km/hr 24 km/hr 0.4 km/hr 2.5 km/hr 0.04 km/hr

Three Kinds of Speed

Speed What is the average speed of a cheetah that sprints 100 m in 4 s? How about if it sprints 50 m in 2 s? 2) If a car moves with an average speed of 60 km/h for an hour, it will travel a distance of 60 km. (a) how far would it travel if it moved at this rate for 4 h? (b) for 10 h?

Speed 2 3) In addition to speedometer on the dashboard of every car is an odometer, which records the distance traveled. If the initial reading is set at zero at the beginning of a trip and the reading is 40 km one half hour later, what has been your average speed? 4) Would it be possible to attain the average speed in previous example and never go faster than 80 km/h?

Velocity Velocity describes the speed and the direction of motion

Instantaneous Velocity

Speed or Velocity? 186,282 mi. / s Speed Velocity

Speed or Velocity? 107 km / h North

Speed or Velocity? 55 mi. / h Speed Velocity

Speed or Velocity? 1300 km / h East

Speed or Velocity? 212 mi. / h Speed Velocity

Velocity With what is the race-car driver concerned, speed or velocity? The speedometer of a car moving to the east reads 100 km/h. It passes another car that moves to the west at 100 km/h. Do both cars have the same speed? Do they have the same velocity? During certain period of time, the speedometer of a car reads a constant 60 km/h. Does this indicate a constant speed or a constant velocity?

Velocity How might you estimate your speed if the speedometer in your car is broken? Which of the following can be used to measure an average speed: stopwatch, odometer, or speedometer? An instantaneous speed?

Acceleration Rate of change of velocity Described as a change in speed over a change in time

∆v a ∆ t Acceleration Formula ∆v Change in speed a = acceleration ∆ t Change in time ∆v a ∆ t

∆ vfinal – vinitial vf - vi “change in” Greek letter Delta Always described as the final condition minus the initial condition “Change in speed” vfinal – vinitial vf - vi

a vf - vi tf - ti Acceleration Formula vf - vi a = acceleration

Acceleration

Two ways to accelerate Change speed Change direction Speed up Slow down Change direction Remember that velocity is speed and direction Changing speed or direction is acceleration Acceleration can be negative (deceleration), depending on the change in the frame of reference

Motion under Constant Acceleration Acceleration is the change per second of the velocity v = at vf = vi + at vf = √vi2 + 2ad d = vi + ½at2 ⊽ = (vf + vi) / 2

Which has the greater acceleration, an airplane that goes from 1000 km/h to 1005 km/h in 10 s, or a skateboard that goes from 0 to 5 km/h in 1 sec? What is the acceleration of a race car that whizzes past you at a constant velocity 400 km/h? How far will a car slide if it’s going 108 km/h and slams on the brakes ( – 8 km/h/s)? If you’re running at 12 m/s and you accelerate at 0.33 m/s for 6 s, how fast are you going?

Observed Constant Acceleration Gravity is the attraction of one mass toward any other mass. It decreases over distance Explains why the Moon has more gravitational effect on the Earth than the Sun Here, gravity is a constant acceleration downward (toward the center of the Earth)

Falling Objects

Acceleration on Galileo’s Inclined Planes Galileo found greater accelerations for steeper inclines. The ball attains max acceleration when the incline is tipped vertically.

Galileo’s Observations a ball rolling down an inclined plane is moving with constant acceleration greater accelerations for steeper planes, max acceleration when incline is tipped vertically regardless of weight and size, when air resistance is small enough to be neglected, all objects fall with the same unchanging acceleration

At a given location on the Earth and in the absence of air resistance, all objects fall with the same, constant acceleration

What a drag! It is common observation that many objects fall with unequal accelerations: a leaf, a feather or a sheet of paper may come to the ground slowly. Why? Air resistance is the friction of air particles on an object moving through it

FEATHER DROP ON MOON

g Acceleration due to gravity On Earth, g has a value of 9.8m/s2 g will change if: The object gets farther from the center of the Earth The object’s mass changes (would have to be a BIG change in relation to the Earth)

Flying Cats A cat steps off a ledge and drops to the ground in ½ second. What is its speed (vf) on striking the ground? What is its average speed during the ½ second? What is the height of this ledge?

Questions, you have? Which of the following (if any) could not be considered an “accelerator” in an automobile: gas pedal, brake pedal, steering wheel?

Questions, you have? A sports car accelerates from 65 mph to 75 mph in 2 seconds while a minivan accelerates from 20 mph to 35 mph in 2 seconds. Which one has the larger acceleration?

Questions, you have? You are standing on a high cliff above the ocean. You drop a pebble, and it strikes the water 4 seconds later. Ignoring the effects of air resistance, how fast was the pebble traveling just before striking the water? What is the height of the cliff?