Motion Introduction Notes

1. Unit 1 - MotionUnit 1 - Motion

2. I.I. Rates:Rates:
 The amount of some change (∆)The amount of some change (∆)
per unit time.per unit time.
 changechange
tt

3. II.II. Speed and Velocity (v)Speed and Velocity (v)
A.A. SpeedSpeed - the rate of distance- the rate of distance
traveled per time relative to sometraveled per time relative to some
point.point.
1.1. Instantaneous Speed - speed atInstantaneous Speed - speed at
some momentsome moment
2.2. Scalar quantityScalar quantity
(magnitude)(magnitude)

4. 3)3) Avg. Speed = totalAvg. Speed = total distance traveleddistance traveled
total timetotal time
distance traveled

5. B.B. VelocityVelocity - displacement- displacement
timetime
displacement

6. B.B. VelocityVelocity - displacement- displacement
timetime
average velocityaverage velocity: most measurements: most measurements
are avg. vare avg. v
displacement
units:units: mm
ss
vvavgavg == ∆d∆d
∆t∆t
Vector quantity (magnitudeVector quantity (magnitude andand
direction)direction)

7. displacement vs. distance traveleddisplacement vs. distance traveled
OdometerOdometer
measurementmeasurement
SpeedSpeed
Distance fromDistance from
starting tostarting to
ending pointending point
(as the crow(as the crow
flies)flies)
VelocityVelocity

8. C.C. instantaneous velocity:instantaneous velocity: vv
 the slope of a tangent line at anythe slope of a tangent line at any
point on a d-t graphpoint on a d-t graph
d
t
Velocity atVelocity at
time ttime t11
t1

9. D.D. Change in VelocityChange in Velocity
1)1) Velocity equals speed whenVelocity equals speed when
moving in amoving in a straight linestraight line..
(Cruise control on straight(Cruise control on straight
highway)highway)

10. 2)2) Velocity changes if speedVelocity changes if speed oror
direction changes.direction changes.
gas pedalgas pedal
brakesbrakes
turn steering wheelturn steering wheel

11. ExampleExample
1 2
Boat 1 is traveling with a speed of 10 mph.Boat 1 is traveling with a speed of 10 mph.
Boat 2 is traveling with a speed of 15 mph.Boat 2 is traveling with a speed of 15 mph.
a.a. Compare the speed of these two boats.Compare the speed of these two boats.
b.b. Compare the velocity of these twoCompare the velocity of these two
boats.boats.

12. E.E. AccelerationAcceleration --
 Change in velocity over timeChange in velocity over time
 a =a = ∆v∆v = v= vff-v-voo
∆t∆t ∆t∆t
Units:Units: m/sm/s
ss
== mm
ss22

13. E.E. AccelerationAcceleration --
 Change in velocity over timeChange in velocity over time

14. E.E. AccelerationAcceleration --
direction is important -> vectordirection is important -> vector
quantityquantity
What does a positive acceleration
mean?
What does a negative acceleration
mean?

15. III.III. Acceleration of GravityAcceleration of Gravity
(neglecting air resistance)(neglecting air resistance)
 everything accelerates
to the center of the
earth at the same rate.
 g = 9.81 m/s2
(labs)
 10 m/s2
(calculations)

16. IV.IV. Graphing Distance vs TimeGraphing Distance vs Time
d
t
A. (position(position
graph)graph)

17. IV.IV. Graphing Distance vs TimeGraphing Distance vs Time
d
t
A. (position(position
graph)graph)
B.The slope of a line on a d vs. t
graph is the velocity, v, of the
object.

18. d
t
Slope = rise
run
= ∆y
∆x
= ∆distance
∆time
= v

19. D
I
S
T
A
N
C
E
TIME
11
22
33
1: Slope (+), v (+), moving away
2: Slope (-), v (-), moving towards
3: Slope = 0, v = 0 not moving
C.

20. V.V. Average speed & average velocityAverage speed & average velocity
A. Avg. speed = total distance traveled
total time
B. Avg. v = total displacement
total time
where displacement = net
movement

21. ex) A horse runs south at 4m/s for 30s , stopsex) A horse runs south at 4m/s for 30s , stops
for 10s, then runs north at 2m/s for 30s.for 10s, then runs north at 2m/s for 30s.
What are the average speed and averageWhat are the average speed and average
velocity of the horse? Draw a d-t graph.velocity of the horse? Draw a d-t graph.
Givens:
v2 = 0
t2 = 10s
v3 = -2m/s (North)
t3 = 30s
v1 = 4m/s (South)
t = 30s

22. ex) A horse runs south at 4m/s for 30s , stopsex) A horse runs south at 4m/s for 30s , stops
for 10s, then runs north at 2m/s for 30s.for 10s, then runs north at 2m/s for 30s.
What are the average speed and averageWhat are the average speed and average
velocity of the horse? Draw a d-t graph.velocity of the horse? Draw a d-t graph.
speedavg= distance
time
Givens:
v1 = 4m/s
t1 = 30s
v2 = 0
t2 = 10s
v3 = -2m/s
t3 = 30s
d1=(4m/s)(30s)=120m
d2=0m
d3=(2m/s)(30s)=60 m
= d1 + d2 + d3
t1 + t2 + t3
= 120m+0m+60m
30s+10s+30s
= 180m
70s
= 2.6m
s

23. ex) A horse runs south at 4m/s for 30s , stopsex) A horse runs south at 4m/s for 30s , stops
for 10s, then runs north at 2m/s for 30s.for 10s, then runs north at 2m/s for 30s.
What are the average speed and averageWhat are the average speed and average
velocity of the horse? Draw a d-t graph.velocity of the horse? Draw a d-t graph.
vavg = ∆d
t
Givens:
v1 = 4m/s
t1 = 30s
v2 = 0
t2 = 10s
v3 = -2m/s
t3 = 30s
= 60m
70s
Goes out 120m, comes back 60 m
∆d = 60m
= 0.86m South
s

24. ex) A horse runs south at 4m/s for 30s , stops for 10s, then runs north at 2m/sex) A horse runs south at 4m/s for 30s , stops for 10s, then runs north at 2m/s
for 30s. What are the average speed and average velocity of the horse? Draw afor 30s. What are the average speed and average velocity of the horse? Draw a
d-t graph.d-t graph.
Givens:
v1 = 4m/s
t1 = 30s
v2 = 0
t2 = 10s
v3 = -2m/s
t3 = 30s
120
80
40
0
0 10 20 30 40 50 60 70
d
t

25. VI.VI. Graphing MotionGraphing Motion
A. d vs t Graphs - Slope = ∆d/∆t = v
B. v vs. t graphs - Slope = ∆v/∆t = a
Area = (v)(t) = ∆d
C. a vs. t graphs - Area = (a)(t) = ∆v

26. Ex) What’s Happening?
v
t
1
2
3
4
5
6
7
8
What would the d-t graph
look like?
What would the a-t graph
look like?

27. ex) A car traveling 20 m/s requires
5 s to accelerate to 35 m/s.
Find the acceleration of the car?
How far does it travel?
(draw all graphs)

28. D. Draw in the
remaining graphs
for:
(1) Assume
original position
is at 0 m.
d
tv
t
a
t

29. (2)
Assume
original
position is
at 0 m and
vo = 0 m/s.
t
d
v
t
a
t

30. E. Draw d vs t, v vs t, & a vs t graphs
for the following scenarios
(1) A car starts from a
stop and
accelerates for 5 s
at 4 m/s2
, then
drives at a
constant velocity
for 5 s more. The
car then brakes to
a hard stop in 2 s.

31. E. Draw d vs t, v vs t, & a vs t graphs
for the following scenarios
(2) A train travels at 10 m/s for 6 s and
then accelerates at 2 m/s2
for three
seconds. The train then moves at a
constant
velocity for
5 s. It then
slows to a
stop at a
rate of
-4 m/s2
.

32. VII. Freefall
A. Refers to motion of an object moving
vertically through the air (UP or DOWN)
B. No other forces are considered except
GRAVITY.
So ……. a = -10m/s2
C. When stepping out of a plane or dropping a
rock: vo = 0 m/s
D. What goes up ……… must come down
AND must come down at the same speed
but opposite direction as it went up.

33. ex1) A train traveling at an original
velocity of 78 m/s accelerates at a rate
of 20 m/s2
for 7 s. Draw all three
graphs.
a) What is the velocity of the train at the end of
7 s?
b) How far does the train travel in those 7 s?

34. ex2) A ball is thrown upward at a
speed of 45 m/s. Due to gravity, the
ball accelerates downward (decelerates)
at 10 m/s2
.

35. ex2) A ball is thrown upward at a
speed of 45 m/s. Due to gravity, the
ball accelerates downward (decelerates)
at 10 m/s2
.
a) Find the velocity 3 s after it is released.
b) Find the velocity 6 s after it is released.
c) Where is the ball at 6 s after release?
d) What is the maximum height the ball
reaches? (vf = 0 m/s)

36. ex3) Ignoring air resistance, find the
distance fallen when a skydiver reaches
88 m/s? (200 mph)

37. ex 4) A parked car is left in neutral at
the top of a hill and begins to roll. If the
car accelerates at 3 m/s2
down the hill:
a) How long will it take to roll 200 m?
b) What will its velocity be?