Remeber this? You still need to know this!!! Motion: Speed: Measure of how fast something is moving Speed = Distance Time Speed is a rate: something divided by time SI units for Speed: (m/s) Instantaneous Speed vs Average Speed Instantaneous Speed speed at any given moment of time Average Speed total distance covered over a time interval Speed is scalar (magnitude but no direction) Velocity is a vector (magnitude and direction) Speed: 1) Scalar Magnitude only Velocity: 1) Vector Magnitude & Direction Distance: How far you travel. Motion: Displacement: How far you are from where you began (your POSITION). SPEED Example: Given: S = 12 m / s t = 10. s Find: d =??? t x S avg = d x t t St = d a = Δ v Δt Change in velocity Change in time Gravity is an acceleration Gravity = 9.8 m / s 2 d = St d = (12 m / s)(10. s) = 120 m Acceleration: Units: m s 2 Ways to Accelerate: Speed up Slow down Change direction 2) Savg = d t Savg = average speed t = time d = distance 2) vavg = vavg = average velocity t = time d t d = DISPLACEMENT ACCELERATION Example: If my car accelerates from 25 m / s to 30 m / s in 2.0 seconds, what is its acceleration? Δv a = = Δt UNITS: v 2 v 1 t 2 t 1 m / s s == = m s 30 m / s 25 m / s 2.0 s 0.0 s x x 1 s == m s 2 = 2.5 m / s s a = 2.5 m / s2
Review: Scalar = magnitude = 'how much' Examples: Fish sticks are gross!!! 1kg Mass Volume Time
Speed! Velocity! It's time to examine the difference.
Speed: 1) Scalar Magnitude only 2) S avg = S avg = speed t = time d t d = distance Velocity: 1) Vector Magnitude & Direction 2) v avg = v avg = t = time d t average velocity d = DISPLACEMENT
What's the Difference??? Distance: How far you travel. Displacement: How far you are from where you began.
Vector examples: If this did happen, what would be the DISPLACEMENT of the Rocket? d = v i t + 1 / 2 at 2
Vector examples continued...
Vector examples continued... Bring it!!! Oh, its getting' brought!!!
If you haven't guessed yet, we draw vectors in physics as arrows. They usually have a scale. 60 km/h Would we read this as: 60 km/h 'up' or 60 km/h 'North'? NOT THIS KIND OF SCALE
If you haven't guessed yet, we draw vectors in physics as arrows. They usually have a scale. 60 km/h Would we read this as: WARNING: THESE ARE NOT THE SAME 60 km/h 'up' or 60 km/h 'North'?
If you haven't guessed yet, we draw vectors in physics as arrows. They usually have a scale. Direction depends on how it is referenced! 60 km/h
Question 1: What is the scale of this vector? 60 km/h a) 3 m = 60 km/h b) 1 cm = 20 km/h Centimeters (cm) c) 1 cm = 15 km/h d) I have no idea 1 A B C D
Question 1: What is the scale of this vector? 60 km/h a) 3 m = 60 km/h Centimeters (cm) b) 1 cm = 20 km/h c) 1 cm = 15 km/h d) I have no idea Since the arrow is 3 cm long, and the vector magnitude is 60 km/h. Divide 60/3 = 20 km/h for every cm of length.
Scalar Quantities can be added, subtracted, multiplied, divided, just like 'normal' numbers. Example: 10 kg + 20 kg = 30 kg Vectors can also be added, subtracted, multiplied, divided, but not like normal numbers. With vectors, 1 + 1 = 2, sometimes, but not always. It can change. WHY???
Question 2: An airplane travels north. A tailwind also blows north. The velocity of the plane will: 2 A B C D Tailwind a) Decrease b) Increase c) Stay the same d) I have no idea
Question 2: An airplane travels north. A tailwind also blows north. The velocity of the plane will: = a) Decrease Tailwind b) Increase c) Stay the same d) I have no idea
Question 3: Using the scale of 1 cm = 40 km/h, how fast is the plane traveling relative to the ground? a) 120 km/hr b) 40 km/h Centimeters (cm) Tailwind 3 A B C D c) 160 km/h d) I have no idea
Question 3: Using the scale of 1 cm = 40 km/h, how fast is the plane traveling relative to the ground? a) 120 km/hr b) 40 km/h Centimeters (cm) Tailwind c) 160 km/h d) I have no idea (3 cm X (40 km/h)/cm) + (1 cm X (40 km/h)/cm) 120 km/h + 40 km/hr 160 km/hr
Centimeters (cm) Question 4: Using the scale 1 cm = 40 km/h, how fast does the plane travel relative to the ground with the head wind? a) 100 km/hr Headwind b) 40 km/h 4 c) 160 km/h A B C D d) 120 km/h
Centimeters (cm) Question 4: Using the scale 1 cm = 40 km/h, how fast does the plane travel relative to the ground with the head wind? a) 100 km/hr Headwind b) 40 km/h = (3 cm X (40 km/h)/cm) (2 cm X (40 km/h)/cm) 120 km/h 80 km/hr 40 km/hr c) 160 km/h d) 120 km/h
Question 5: Suppose our plane is flying at 40 km/hr north and encounters a wind blowing at 30 km/hr from the west. The wind will cause the plane's velocity to: N 5 a) Increase b) Decrease c) Stay the same A B C D
Question 5: Suppose our plane is flying at 40 km/hr north and encounters a wind blowing at 30 km/hr from the west. The wind will cause the plane's velocity to: N The blue line is the longest!!! a) Increase b) Decrease c) Stay the same
Question 6: Suppose our plane is flying at 40 km/hr north and encounters a wind blowing at 30 km/hr from the west. What will be the plane's speed? N 6 a) 50 km/hr b) 60 km/h c) 70 km/h A B C D
Question 6: Suppose our plane is flying at 40 km/hr north and encounters a wind blowing at 30 km/hr from the west. What will be the plane's speed? N c b a 2 + b 2 = c 2 a (30 km/h) 2 + (40 km/h) 2 = c 2 c 2 = 2500 km 2 /h 2 c = 50 km/hr a) 50 km/hr b) 60 km/h c) 70 km/h
Question 7: George Washington (G Dub a Dub), is having trouble finding the British. In his search to kick some red coat tail, he first goes 100 km north, 40 km east, realizes he is off course, then turns south for 50 km, finally finding the enemy. How much distance has he covered? N a) 100 km b) 190 km c) 200 km 7 A B C D
Question 7: George Washington (G Dub a Dub), is having trouble finding the British. In his search to kick some red coat tail, he first goes 100 km north, 40 km east, realizes he is off course, then turns south for 50 km, finally finding the enemy. How much distance has he covered? N 40 km 50 km a) 100 km 100 km b) 190 km c) 200 km 100 km + 40 km + 50 km = 190 km
Question 8: George Washington (G Dub a Dub), is having trouble finding the British. In his search to kick some red coat tail, he first goes 100 km north, 40 km east, realizes he is off course, then turns south for 50 km, finally finding the enemy. How far is he from where he started? N 40 km 50 km 100 km 8 2 sig-figs
Question 8: George Washington (G Dub a Dub), is having trouble finding the British. In his search to kick some red coat tail, he first goes 100 km north, 40 km east, realizes he is off course, then turns south for 50 km, finally finding the enemy. How far is he from where he started? N 100 km 40 km 50 km The question asks you to calculate: DISPLACEMENT This is called the Displacement. 2 sig-figs
40 km 100 km 50 km
? = (50 km) 2 + (40 km) 2 64m 100 km 40 km 50 km 50 km 40 km?
B. Displacement is independent of path. A.
Tip to Tail Method: Let's add these vectors:
Tip to Tail Method: Let's add these vectors: Start R Finish
Tip to Tail Method: One of you add these vectors:
Tip to Tail Method: One of you add these vectors: Start R Finish The Resultant Vector will always be the same as long as the original vectors are added tip to tail!!!