1. PHYSICS UNIT 1: KINEMATICS (Describing Motion)

2. MOTION ALONG A LINE
Who’s Upside Down?

3. MOTION ALONG A LINE
Who’s Moving?

4. MOTION ALONG A LINE
Motion: change in position of an object compared to a frame of reference (a "stationary" reference point)
Measuring Motion (along a line)
position, x: location with respect to the origin The origin is (x=0), unit: m
displacement, s = Dx : change in position
Dx = xf – xi displacement = final position – initial position

5. MOTION ALONG A LINE
displacement examples

6. MOTION ALONG A LINE
time, t: time since motion start, unit: s (text uses Dt)
velocity, v: time rate of displacement, unit: m/s
average velocity, vav = (xf-xi)/t
has same +/- sign as displacement – shows direction of motion along line
instantaneous velocity, v: actual velocity at a specific point in time, slope on an x vs. t graph.
at constant speed, v=vav
for changing speed, vvav

7. MOTION ALONG A LINE Speed: the amount of velocity S=d/t
Velocity is speed and direction (+/- along a line), speed doesn’t have direction. V=∆x/t
a velocity of -24 m/s is not the same as +24 m/s (opposite directions), but both have the same speed (24 m/s).
car speedometer indicates speed only; for velocity, you would need a speedometer and a compass.

8. SOLVING PROBLEMS Problem-Solving Strategy
Given: What information does the problem give me?
Question: What is the problem asking for?
Equation: What equations or principles can I use to find what’s required?
Solve: Figure out the answer.
Check: Do the units work out correctly? Does the answer seem reasonable?

9. GRAPHING MOTION interpreting an x vs. t (position vs. time) graph
constant +v
constant v = 0
constant –v
changing +v
changing +v
(moving forward)
(not moving)
(moving backward)
(speeding up)
(slowing down)

10. GRAPHING MOTION slope = rise/run = Dx/Dt, so slope = vav
interpreting an x vs. t (position vs. time) graph
for linear x vs. t graphs: x t
slope = rise/run = Dx/Dt, so
rise = Dx
slope = vav
run = Dt

11. GRAPHING MOTION slope of tangent line = vinstantaneous
interpreting an x vs. t (position vs. time) graph
for curving x vs. t graphs: x t
slope of tangent line = vinstantaneous

12. GRAPHING MOTION interpreting a v vs. t (velocity vs. time) graph
constant +v
constant v = 0
constant –v
changing +v
changing +v
(slowing down)
(moving backward)
(speeding up)
(moving forward)
(not moving)

13. GRAPHING MOTION
comparing an x vs. t and a v vs. t graph

14. ACCELERATION
constant velocity
constant acceleration

15. ACCELERATION Acceleration, a: rate of change of velocity
unit: (m/s)/s or m/s2
speed increase (+a), speed decrease (–a), change in direction (what are the three accelerators in a car?)
average acceleration, aav = (v-u)/t = Dv/t
instantaneous acceleration, a: actual acceleration at a specific point in time

16. ACCELERATION Constant acceleration (a = aav) v  t, x  t2
example: a=2 m/s2
time (s) 1 2 3 4 5 6 2 4 6 8 10 12
speed (m/s)
position (m) 1 4 9 16 25 36
v  t, x  t2

17. ACCELERATION terms: terms: t: elapsed time xf : final position
xo: initial position
s: change in position (xf-xi)
terms:
a: acceleration
vavg: average velocity
vf: final velocity
u, vo: initial velocity
Dv: change in velocity (v-u)

18. ACCELERATION defined equations: a = Dv/t vav = Dx/t vav = (v+u)/2
derived equations:
s = ½(v+u)t
v = u + at
xf = xi + ut + ½at2
v2 = u2 + 2as

19. GRAPHING MOTION interpreting a v vs. t (velocity vs. time) graph
For linear v vs. t graphs, slope = a
constant a = 0
constant +a
constant –a
(speeding up)
(slowing down)
(constant speed)

20. GRAPHING MOTION
comparing v vs. t and a vs. t graphs

21. UNIT 1: KINEMATICS (Describing Motion)
PHYSICS
UNIT 1: KINEMATICS
(Describing Motion)

22. FREE FALL
Free Fall: all falling objects are constantly accelerated due to gravity
acceleration due to gravity, g, is the same for all objects
use y instead of x, up is positive
g = –9.80 m/s2 (at sea level; decreases with altitude)

23. FREE FALL
air resistance reduces acceleration to zero over long falls; reach constant, "terminal" velocity.
Why does this occur?
Air resistance is proportional to v^2

24. UNIT 1: KINEMATICS (Describing Motion)
PHYSICS
UNIT 1: KINEMATICS
(Describing Motion)

25. MOTION IN A PLANE Start at the Old Lagoon Go 50 paces East
Go 25 Paces North
Go 15 paces West
Go 30 paces North
Go 20 paces Southeast
X marks the Spot!

26. MOTION IN A PLANE sine: sin q = opp/hyp cosine: cos q = adj/hyp
Trigonometry
sine: sin q = opp/hyp
cosine: cos q = adj/hyp
tangent: tan q = opp/adj

27. MOTION IN A PLANE Vectors
scalars: only show how much (position, time, speed, mass)
vectors: show how much and in what direction
displacement, r or x : distance and direction
velocity, v : speed and direction
acceleration, a: change in speed and direction

28. MOTION IN A PLANE q v Vectors
arrows: velocity vector v = v (speed), q (direction)
length proportional to amount
direction in map coordinates
between poles, give degrees N of W, degrees S of W, etc. q v N S W E

29. MOTION IN A PLANE
puck v relative to earth = puck v relative to table + table v relative to earth

30. MOTION IN A PLANE Combining Vectors
draw a diagram & label the origin/axes!
Collinear vectors: v v v v2
resultant: vnet=v1+v (direction: + or –)
ex: A plane flies 40 m/s E into a 10 m/s W headwind. What is the net velocity?
ex: A plane flies 40 m/s E with a 10 m/s E tailwind. What is the net velocity?

31. MOTION IN A PLANE Perpendicular vectors: resultant’s magnitude:
resultant’s direction:

32. UNIT 1: KINEMATICS (Describing Motion)
PHYSICS
UNIT 1: KINEMATICS
(Describing Motion)

33. UNIT 1 TEST PREVIEW Concepts Covered: motion, position, time
speed (average, instantaneous)
x vs. t graphs, v vs. t graphs, a vs. t graphs
vectors, scalars, displacement, velocity
adding collinear & perpendicular vectors
acceleration
free fall, air resistance

34. UNIT 1 TEST PREVIEW What’s On The Test:
21 multiple choice, 12 problems
Dx = ½(vf+vi)t vf = vi + at
xf = xi + vit + ½at2 vf2 = vi2 + 2aDx