1. Speed Velocity and Acceleration
Everything You Need To Know About Motion

2. Motion Motion is just a change in position.
To describe how an object moves you need
A ruler to measure where an object is.
And a clock to measure when an object is.

3. Here is a little bug located at 0 cm at 0 seconds.

4. 10 seconds later he is at 50 cm.

5. SPEED
The speed of the bug is just his distance traveled divided by how long it takes.
Speed = distance/time
Speed = 50 cm/10 s = 5 cm/s

6. Speed is just how fast something is moving.
Speed is always a positive number.
Quantities that can be described by a single number are called scalars.

7. MORE SCALARS
TEMPERATURE
VOLUME
MASS
STUDENTS IN A ROOM
ENERGY

8. VELOCITY Velocity is speed and direction.
Velocity is how fast and which way.
Quantities that have direction are called vectors.

9. MORE VECTORS
ACCELERATION
FORCE
DISPLACEMENT
MOMENTUM

10. Suppose our bug starts off at 100 cm.

11. And ends up at 80 cm 10 seconds later.

12. Velocity = change in position/time
Calculating velocity is a little more complicated than calculating speed.
Velocity = change in position/time
Velocity = (final position – initial position)/time
Velocity = (80cm – 100cm)/10 seconds
Velocity = - 2 cm/s

13. For objects moving along a straight line
A positive velocity means moving to the right. (usually)
A negative means moving to the left. (usually)

14. A negative velocity does not mean an object is moving slower than zero cm/s.
You can’t move slower than standing still.
It just means an object is moving in a certain direction.

16. ACCELERATION Acceleration is a change in velocity.
So an object accelerates if it
Speeds up
Slows down
Or changes the direction it is moving,

17. Acceleration = change in velocity/time
Acceleration = (final velocity – initial velocity)/time
Acceleration has units of
velocity/time
(meters per second)/seconds
Or m/s/s or m/s2

18. confusion Acceleration, like velocity, has direction.
For objects moving along a straight line the direction of an object’s acceleration is denoted by plus or minus.

20. Acceleration = (30 m/s – 0 m/s)/10 s
a = 3 m/s/s
The car’s velocity is increasing 3 m/s per second.
The car is accelerating towards the right.

22. a = (0m/s – 20 m/s)/10 s
a = - 2 m/s/s
Although the car is moving to the right
It is accelerating to the left!

24. a = (final velocity – initial velocity)/time
a = ( -30 m/s – 0 m/s)/ 10 s
a = - 3 m/s/s
The car is both moving to the left and accelerating to the left.
Negative acceleration does not always mean an object is slowing down!

29. Newton’s 3 laws of motion
Isaac Newton

30. 1st Law: Law of Inertia
A body at rest tends to stay at rest, a body in motion tends to keep moving along at a constant speed and in a straight-line path unless interfered with by some external forces.

31. example

32. Motorcycle crash dummy

33. Another example (watch the ladder)

34. 2nd Law: F=ma
The acceleration of a body is directly proportional to the net force acting on it and inversely proportional to its mass.The direction of the acceleration is in the direction of the applied force.

35. Directly proportional to Force
Small force
Small acceleration
Large force
Large acceleration

36. inversely proportional to mass
Beach
ball
Bowling
ball
small mass
Large acceleration
Large mass
Small acceleration

37. “Inertial” mass
“Inertial” mass, mi, is the resistance to changes in the state of motion
Objects with large mi
are hard to get moving
(& once started, hard
to stop),
Objects with small mi
easier to get moving
(& easier to stop),

38. Units again! (we cant avoid them!)
Mass: basic unit = 1kilogram = 1kg
mass of 1 liter (1.1 quarts) of water
10cm
This much
water!
10cm
10cm

39. Slide tail of one to tip of the other (keep directions fixed)
Net force
Tip-to-tail method
for adding vector
Net force is the vector from the tail of the 1st to the tip of the 2nd. (0 in this case).
Slide tail of one to tip of the other (keep directions fixed)

40. Tip-to-tail method Net force points down the hill
Slide tail of one to tip of the other (keep directions fixed)

41. Newton’s 2nd law  F=ma a  F a  F a  1/m a  F/m a = F/m
a is proportional to F:
a  F
direction of a
= direction of F:
a  F
a is inversely
proportional to m:
a  1/m
combine:
a  F/m
multiply
both sides
by m
set proportionality
constant = 1:
a = F/m

42. Weight = Force of gravity
Free-fall acceleration of a beach ball
& a bowling ball are the same: a=g m M
Beach
ball
Bowling
ball
F2 = Ma
a = g
F1 = ma
a = g
Bowling ball has more inertia: M > m
Force of gravity must be larger on the bowling ball
by a factor that is proportional to mass

43. Weight is proportional to mass
Newton’s 2nd law: F=ma
If gravity is the only force: F = W
a = g
W = mg
acceleration
due to gravity
weight
“gravitational”
mass

44. Two different aspects of mass
Force of gravity is proportional to “gravitational” mass
mgg
Weight: W = m g
Newton’s 2nd law:
Inertia; resistance to changes in state is proportional to “inertial” mass F m
a = mi
Experiment shows: mg = mi

45. Units of Force F=ma m kg s2 1 pound =1lb = 4.5 N
Unit of force: 1 Newton = 1N = 1 kg m/s2
1 pound =1lb = 4.5 N

46. What is your mass? F=ma W=mg a=g m= W W g Weight = force of
Earth’s gravity on you
Suppose I
jump off
a tqble
F=ma
W=mg
a=g m= W g W

47. Kgf =“kilogram force” = 9.8 N
!!!!!
Mass & weight
“weight” = 85 kg
kg is a unit of mass, not force
“my weight”
Convert to Newtons:
W = 85 kg x 9.8m/s2 = 833 N =
Units of N
kg m/s2
Kgf =“kilogram force” = 9.8 N

48. Newton’3rd Law: action-reaction
Whenever one object exerts a force on a second object, the second object exerts an equal in magnitude but opposite in direction force on the first.
reaction: the
canoe pushes
me forward
action: I push
on the canoe

49. Action Reaction

50. I push on the bus
v= 0 F

51. But I accelerate v Newton:
The bus exerted an “equal but opposite” force on me.

52. This force tries to accel.
Look again
All forces come in pairs! -F F
This force causes me
to accelerate backwards
This force tries to accel.
the bus forward

53. Air-filled balloon reaction: air pushes on balloon action: balloon
pushes on air

54. opposite force on the gun F1
recoil
action: gun exerts
force F2 on bullet
making it accelerate
reaction: equal but
opposite force on the gun F1
Produces a recoil

55. Rocket propulsion reaction: rocket gets pushed in the opposite
direction
action: rocket engine
pushes exhaust
gasses out the rear