Chapter-2 Linear Motion 2.1 Motion is Relative Q: Is the pencil sharpener moving? A-1:Yes, relative to the sun, stars, universe. Since the Earth is always moving relative to the sun, so does anything on the Earth. A-2: No, relative to the wall.

2.2 SPEED 2.2 SPEED Speed = ? A measure of how fast something is moving. distance coveredd distance coveredd Speed = unit of time = t Any combination of distance and time can be used. mi/hr (mph), km/s, m/s, cm/yr, ft/s

Instantaneous Speed = How fast an object is moving at a particular instant in time. Instruments used to measure instantaneous speed Ex: = Speedometer, radar gun, tachometer

Average Speed = total distance traveled Average speed = total time of travel d Avg speed = t

Example #1 The speedometer in every car also has an odometer that records the distance traveled. If the odometer reads zero at the beginning of a trip and 20km 15 minutes later, what is the average speed? 20km Avg speed = 0.25hr = 80km/hr

Would it be possible to attain this average speed and never exceed a reading of 80km/hr on the speedometer? Explain. NO, the car would have to start from rest,  at some point the car would have to reach a speed greater than 80km/hr.

Example #2 If an eagle can maintain a constant speed of 40m/s, it will travel 40 meters every second. At this rate, how far will it travel in 10 seconds? In 1 minute? d Avg speed = t  d = avg speed x time d = 40m/s x 10s = 400m d = 40m/s x 60s = 2400m

2.3 Velocity (v) Does speed = velocity? In everyday language, yes, you can use them interchangeably. However, in physics, NO, they cannot be used interchangeably. Velocity (v)= ? Speed with direction Ex: 24 m/s N, 15mph SW, 39 km/hr →

Constant velocity = ? Constant speed and direction. Ex: 37m/s in a straight line. Change in velocity = A change in speed or a change in direction.

2.4 ACCELERATION Acceleration (a) = ? The rate of change in velocity. Ex: the object could speed up, slow down and/or change direction.  a could be either (+) or (-) Δv v f - v i Δv v f - v i a = Δt = t f – t i

Example - 1 A car is traveling at 20m/s, it speeds up to 60m/s in 8s. What is its acceleration? Δv v f – v i 60m/s – 20m/s Δv v f – v i 60m/s – 20m/s a = Δt = t f – t i = 8s - 0s 40m/s a = 8s = 5m/s 2

Example - 2 A jogger is running at 10m/s, she stops in 2 seconds. What is her acceleration? Δv v f – v i 0m/s – 10m/s Δv v f – v i 0m/s – 10m/s a = Δt = t f – t i = 2s - 0s -10m/s -10m/s a = 2s = -5m/s 2

Example - 3 A motorcycle is traveling north at 55m/s for 11 seconds. What is its acceleration? 0m/s 2 Why? Because there was NO change in the motorcycle’s velocity.

List examples of objects that are accelerating: A) an object increasing its speed B) an object decreasing its speed C) an object changing its direction

List examples of objects that are not accelerating A) an object standing still B) an object traveling at a constant speed and direction.

Is the Earth accelerating? The Earth moves at a constant 66,660mph around the sun.

2.5 FREE FALL Free Falling Object = When gravity is the ONLY force acting on an object, causing it to move (fall), the object is said to be in “free fall”. Equation for acceleration = Δv v f - v i Δv v f - v i a = Δt = t f – t i

WHITE BOARD ACTIVITY Do the dropped spheres accelerate? accelerate? If so, at what rate? Calculate. Use the velocity Use the velocity table on the table on the next slide to next slide to calculate the calculate the acceleration. acceleration.

Time Elapsed/Speed Table Elapsed Time SpeedAcceleration 0s0M/s0m/s2 1s9.8m/s? 2s19.6m/s? 3s29.4m/s? 4s39.2m/s? 5s49m/s? 6s58.8m/s? 7s68.6m/s?

What is the acceleration of a free falling object? a = 9.8m/s 2 Since the acceleration is towards the center of the Earth (downward), the acceleration of a “Free Falling” object due to gravity is -9.8m/s 2.

Instantaneous Velocity (speed) Equation

v = v i + at Where: v = instantaneous speed (vel) a = acceleration a = acceleration t = elapsed time t = elapsed time v i = initial velocity v i = initial velocity When an object is in “Free Fall”, the acceleration is due to gravity  the acceleration due to gravity is –g or numerically –g = -9.8m/s 2

So, when an object is in “Free Fall” v = v i + -gt v = v i + (-9.8m/s 2 )t

Example Instantaneous Speed Calculate the velocity of a ball tossed into the air that returns to the thrower’s hand at the same elevation.

The ball leaves the hand at 45m/s. Calculate the velocity after 1s, 2s, 3s, 4s, 5s and 6s. 1s vel = 35.2m/s 2s vel = 25.4m/s 3s vel = 15.6m/s 4s vel = 5.8m/s 5s vel = -4m/s 6s vel = -13.8m/s

What is the velocity of the ball when it returns to the hand? -45m/s, the same speed, but opposite direction, as the ball was thrown.

How long does it take for the ball to reach its highest point? v = v i + at v = v i + -gt 0 = 45m/s + (-9.8m/s 2 )t -45m/s = -9.8m/s 2 t -45m/s -45m/s -9.8m/s 2 = t t = 4.59s

2.6 Free Fall: How Far An object is dropped from a cliff. What is its speed/velocity after 1s? A: 9.8m/s, -9.8m/s How far did the object fall during the first second?

Q: How is the distance traveled each second by a free falling object affected? A: The distance traveled each second increases as the object free falls.  The object is accelerating (Δv). d = v i + 1/2at 2 d = distance traveled a = acceleration v i = initial velocity

How far does the object fall after 1s, 2s, 3s, 4s, 5s, 6s, … d = v i + 1/2at 2

TimeTotal dist fallenDist fallen/sec 0s0m0m 1s4.9m0-1s = 4.9m 2s19.6m1-2s = 14.7m 3s44.1m2-3s = 24.5m 4s78.4m3-4s = 34.3m 5s122.5m4-5s = 44.1m 6s176.4m5-6s = 53.9m

Volunteer $1.00 Reaction Time Lab

2.7 Graphing Motion Graphing Handout “3-pages” Graphing speed vs time.

Graph the velocity data Free Falling Object V = v i + at when v i = 0m/s(dropped) V 1 = 9.8m/s (-9.8m/s) V 2 = 19.6m/s V 3 = 29.4m/s V 4 = 39.2m/s V 5 = 49m/s

Graphing Distance vs Time

Graph the Distance Fallen data Free Falling Object d = v i + ½ at 2 d 1 = 4.9m (-4.9m) d 2 = 19.6m d 3 = 44.1m d 4 = 78.4m d 5 = 122.5m d 6 = 176.4m

2.8 Air Resistance & Free Falling Objects Terminal Velocity = The fastest speed that a free falling object can attain. White Board/Paper Bonus Question. Explain in great detail how/why a free falling object gets to its terminal velocity. One paper per group. You MUST have sketches to support your explanation.