Relative Motion

Frames of Reference Object or point from which motion is determined Object or point from which motion is determined Most common is the Most common is theearth Motion is a change Motion is a change in position relative to a frame of reference

What is motion? If you are standing in one place, and your friend walks by you, are you moving relative to your friend? If you are standing in one place, and your friend walks by you, are you moving relative to your friend? Is your friend moving relative to you? Is your friend moving relative to you? Is either of you moving relative to the earth? Is either of you moving relative to the earth?

Answer: You are moving relative to your friend, and your friend is moving relative to you! You are moving relative to your friend, and your friend is moving relative to you! You are not moving relative to the earth, but your friend is. You are both moving relative to the sun! You are not moving relative to the earth, but your friend is. You are both moving relative to the sun!

What is motion? If you and your friend are walking down the hall together at the same speed, in the same direction, are you moving relative to your friend? If you and your friend are walking down the hall together at the same speed, in the same direction, are you moving relative to your friend? Is your friend moving relative Is your friend moving relative to you? Are either of you moving Are either of you moving relative to the earth?

Answer: You are NOT moving relative to your friend, and your friend is NOT moving relative to you. You both are moving relative to the earth. You are NOT moving relative to your friend, and your friend is NOT moving relative to you. You both are moving relative to the earth.

Uniform motion Uniform motion – occurs when an object is moving at a constant speed/ velocity in a straight line. Constant speed/velocity- means that the object is covering the same distance per unit of time. Scalar – any quantity that is represented by a magnitude and a unit. Vector – any quantity that is represented by a Magnitude, a unit and a direction.

Distance and Displacement Distance (d) is a scalar measure of the actual path between two locations. Distance (d) is a scalar measure of the actual path between two locations. It has a magnitude and a unit. It has a magnitude and a unit. Ex: 50 m, 2.5 hrs. Ex: 50 m, 2.5 hrs. Displacement (d) is a vector measure of the change in position measured in a straight line from a starting reference point. Displacement (d) is a vector measure of the change in position measured in a straight line from a starting reference point. Ex: 5 m [W] Ex: 5 m [W]

Sign Convention In physics we will use a standard set of signs and directions. In physics we will use a standard set of signs and directions. Up, right, east and north are positive directions. ( + ) Up, right, east and north are positive directions. ( + ) Down, left, west, and south are negative directions. ( - ) Down, left, west, and south are negative directions. ( - )

Distance – total trip d total = d 1 + d 2 + d 3 + d 4 d total = 2m + 4m + 2m + 4m d total = 20 m Displacement – change in position d total = + d d d d 4 d total = + 2m + + 4m + - 2m + - 4md total = 0 m

Speed Speed = Change in distance ÷ Time Speed = Change in distance ÷ Time Δ d_ Δ d_ V T Example: A car travels 300km in 6 hours. What is the speed of the car?

Answer: Speed = distance ÷ time Speed = distance ÷ time Speed = 300km ÷ 6 hours Speed = 300km ÷ 6 hours Speed = 50km/hr Speed = 50km/hr

More practice 1. How far can a plane travel if it flies 800km/hr for 9 hours? 1. How far can a plane travel if it flies 800km/hr for 9 hours? 2. How long does it take a ship to go 500 km if it travels at a speed of 50km/hr? 2. How long does it take a ship to go 500 km if it travels at a speed of 50km/hr?

Answer 1. Δ d V T V T Δ d Δ d Δ d Δ d km ▪ 9hrs = 7200km hr hr

Answer 2. Δ d V T V T T 50 T 500km ÷ 50km = 10 hrs hr hr

Instantaneous Speed Instantaneous speed is speed at any instant in time. Instantaneous speed is speed at any instant in time. A speedometer measures speed in ‘real time’ (the instantaneous speed). A speedometer measures speed in ‘real time’ (the instantaneous speed).

Average Speed Average speed is the average of all instantaneous speeds; found simply by a total distance/total time ratio Average speed is the average of all instantaneous speeds; found simply by a total distance/total time ratio The average speed of a trip: The average speed of a trip: V avg = d 1 + d 2 + d 3 + d t 1 + t 2 + t 3 + t

Velocity Speed in a given direction is velocity Speed in a given direction is velocity ( vector). ( vector). What is the velocity of a boat that travels from St. John’s, west to Longpond What is the velocity of a boat that travels from St. John’s, west to Longpond (16 Km ) in 2.5 h ? (16 Km ) in 2.5 h ?

Answer Velocity = displacement ÷ time Velocity = displacement ÷ time Velocity = 16 Km ÷ 2.5 h Velocity = 16 Km ÷ 2.5 h Velocity = 6.4 km/h Velocity = 6.4 km/h Velocity = 6.4 km/h west Velocity = 6.4 km/h west

Change your answer to m/s! = 6.4 km/h ÷ 3.6 = 1.8 m/s Km/hr to m/s conversion trick Km/hr m/s m/s K/hr Divide by 3.6 multiply by 3.6

Difference Between Speed and Velocity Scalar Quantities ( Number and unit) Volume liters Distance Voltage Speed (KM/h) Vector Quantities ( Number, unit and direction) 10 Km West 50 Km/hr south 100 newtons right Velocity (Speed and Direction) Velocity is a Vector Quantity Speed is a Scalar Quantity

Distance-time graphs On your paper, graph the following: On your paper, graph the following: D (m) T (sec) D (m) T (sec)

Was your graph a straight line? A distance-time graph which is a straight line indicates constant speed. A distance-time graph which is a straight line indicates constant speed. In constant speed, the object does not speed up or slow down. The acceleration is zero. In constant speed, the object does not speed up or slow down. The acceleration is zero.

The Steeper the slope the faster the object is moving.

y2y2 y1y1 x1x1 x2x2 On a distance time graph for uniform motion the slope equals the average speed. V avg = Δd Δt

What is the V avg for this graph? = 4 = 2m/s 4 – 2 2

Displacement Time Graphs Like distance time graphs only displacement can be either positive or negative, therefore we need two quadrants. Like distance time graphs only displacement can be either positive or negative, therefore we need two quadrants. dddd tttt Moving left away from origin Moving right toward origin from left Stopped right of origin Stopped left of origin

Graphing ! d t A B C A … Starts at home (origin) and goes right (+) slowly B … Stopped (position remains constant as time progresses) C … Turns around and goes in the (-) direction quickly, passing by home

Explain what is happening for each leg of the trip.

What is the velocity for each leg of the trip? Hint: slope= rise/ run = Δ d = d 2 – d 1 = Avg. velocity t t 2 – t 1

Graph the following on a distance- time graph: d (m)t (s) d (m)t (s)

Was your graph a curve? A graph that curves on a distance-time graph shows that the object is accelerating ( non- uniform motion). A graph that curves on a distance-time graph shows that the object is accelerating ( non- uniform motion). Acceleration. Acceleration.

Distance-time graphs Describe the motion of the object as shown in the Describe the motion of the object as shown in the graph. graph. From 0-8 sec, constant speed: (25 m/sec); From 8-12 sec, no motion (stop); From sec, acceleration; From sec, constant speed

Speed-time graphs Using the distance-time graph from the last frame, draw a speed time graph. First fill in the table below: Using the distance-time graph from the last frame, draw a speed time graph. First fill in the table below: Average Speed (m/s) Time (sec) ____0 to 8 ____8 to 12 ____12 to Draw on board

What does your graph look like? Constant speed will be a horizontal line on a speed time graph. Constant speed will be a horizontal line on a speed time graph. If the speed decreases, the line will slant down. If the speed decreases, the line will slant down. If the speed increases, the line will slant up. If the speed increases, the line will slant up.

On a velocity - time graph the area between the graphed line and the x-axis equals the displacement Area = l x w = 6 s x 30 m/s = 180 m

This object is slowing down in a positive direction. It is non-uniform motion. However we can still calculate the displacement by finding the area of the triangle. ( ½ base x height ) Displacement = ½ base x height = ½ 25.0 m/s x 25.0 s = m Note how the units cancel.

Displacement = area of rectangle + area of a triangle = l x w + ½ base x height = 10.0 s x 5.0m/s + ½ 10.0 m/s x 5.0 s = 50 m + 25 m = 75m Object is moving at a constant speed for 5.0 s then it speeds up for the next 5.0 sec.

Object moving right and speeding up. (+) Object moving left and speeding up. (-) Object moving right and slowing down. (+) Object moving left and slowing down (-)

The slope of the line on a velocity time graph equals the average acceleration. For uniform motion the graph is horizontal, therefore the slope is zero and the acceleration is zero.

Graphing w/ Acceleration d A … Start from rest south of home; increase speed gradually B … Pass home; gradually slow to a stop (still moving north) C … Turn around; gradually speed back up again heading south D … Continue heading south; gradually slow to a stop near the starting point t A B C D

Tangent Lines t SLOPEVELOCITY Positive Negative Zero d On a position vs. time graph: The slope of a tangent line will give the velocity at that point in time. ( instantaneous velocity )

Graphing Tips The same rules apply in making an acceleration graph from a velocity graph. Just graph the slopes! Note: a positive constant slope in blue means a positive constant green segment. The steeper the blue slope, the farther the green segment is from the time axis. a t v t

Area under a velocity graph d t “forward area” “backward area” Area above the time axis = forward (positive) displacement. Area below the time axis = backward (negative) displacement. Net area (above - below) = net displacement. Total area (above + below) = total distance traveled.

All 3 Graphs t d v t a t

What do the following speed-time graphs depict?

Acceleration Change in velocity Change in velocity Can be change in speed or direction Can be change in speed or direction Acceleration = ∆V/ ∆T Acceleration = ∆V/ ∆T ∆V ∆V at at

Acceleration problem A roller coaster’s velocity at the top of a hill is 10m/s. Two seconds later it reaches the bottom of the hill with a velocity of 26m/s. What is the acceleration of the roller coaster? A roller coaster’s velocity at the top of a hill is 10m/s. Two seconds later it reaches the bottom of the hill with a velocity of 26m/s. What is the acceleration of the roller coaster?

Answer Acceleration = ∆V/ ∆T Acceleration = ∆V/ ∆T a = 26m/s – 10m/s a = 26m/s – 10m/s 2 s a = 16m/s 2s 2s a = 8m/s/s or 8m/s 2

More acceleration problems 1. A car accelerates at a rate of 20Km/hr/s. How long does it take to reach a speed of 80 Km/hr? 2. A car travels at 60 Kilometers per hour around a curve. Is the car accelerating? 3. A car travels in a straight line at 60 Km/hr. Is the car accelerating?

Answers: 1. ∆V 80Km/hr a t20Km/hr/ t 4sec = t 2. yes! Because it’s changing direction! 3. no! It’s not changing speed or direction!

Deceleration Negative acceleration Negative acceleration Example: A car slows from 60Km/hr to 20 km/hr in 4 seconds. What is its acceleration? Example: A car slows from 60Km/hr to 20 km/hr in 4 seconds. What is its acceleration?

Answer: Acceleration = ∆V/ ∆T Acceleration = ∆V/ ∆T Acceleration = Vf – Vi Acceleration = Vf – Vi t a = 20km/hr – 60km/hr a = 20km/hr – 60km/hr 4 s a = -40Km/hr 4s 4s a = -10Km/hr/s

Velocity & Acceleration Sign Chart V E L O C I T Y ACCELERATION ACCELERATION Moving forward; Speeding up Moving backward; Slowing down - Moving forward; Slowing down Moving backward; Speeding up

Acceleration due to Gravity 9.8 m/s 2 Near the surface of the Earth, all objects accelerate at the same rate (ignoring air resistance). a = -g = -9.8 m/s 2 a = -g = -9.8 m/s 2 Interpretation: Velocity decreases by 9.8 m/s each second, meaning velocity is becoming less positive or more negative. Less positive means slowing down while going up. More negative means speeding up while going down. This acceleration vector is the same on the way up, at the top, and on the way down!

Motion Graphs – Position vs. Time constant, rightward (+) velocity of +10 m/s a rightward (+), changing velocity - that is, a car that is moving rightward but speeding up or accelerating

Motion Graphs – Velocity vs. Time constant, rightward (+) velocity of +10 m/s a rightward (+), changing velocity - that is, a car that is moving rightward but speeding up or accelerating

Review: Distance-time graph of acceleration

Distance-time graph of deceleration

Review:Speed-time graph of acceleration

Review: Speed-time graph of deceleration

Review: Distance-time graph of constant speed