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Key points in this lecture are: Linear Motion, Speed, Instantaneous Vs Average Speed, Velocity, Acceleration, Free-Fall Topics covered in this course "Basic Concepts of Physics" are: Newton’s Laws of Motion, Linear Motion, Momentum, Energy, Rotation, Gravity, Liquids, Gase, Plasmas, Heat, Waves, Sound, Electrostatics, Electric current, Magnetism, Electromagnetic Induction, Color, Light, Atom and Quantum.
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Preliminaries •
Linear motion is motion in a straight line.
Note that motion is
relative
: e.g. your paper is moving at
107 000 km/hr relative to the sun. But it is at rest relative to you.
Unless otherwise stated, when we talk about speed of thingsin the environment, we will mean relative to the Earth’ssurface.
Speed measures “how fast” :
Units: eg. km/h, mi/h (or mph), m/s
meters per second, standard unitsfor physics
Speed
=
distance
time
Things don’t always move at the same speed, e.g. car starts at0 km/h, speed up to 50 km/h, stay steady for a while, and thenslow down again to stop.
Average speed =
total distance covered
time interval
50 km/h
0 km/h
time
speed
average speed
Velocity is
speed
in a given
direction
(velocity is a vector,
speed is a scalar)
Note that an object may have constant speed but a changing velocityEg. Whirling a ball at the end of a string, in a horizontalcircle – same speed at all times, but changing directions.Or, think of a car rounding a bend, speedometer may notchange but velocity is changing, since direction is.
When there’s just one direction of interest (up or down), often indicate direction by + or -.
Measures how quickly
velocity changes
Acceleration =
change of velocity
time interval
E.g. We feel acceleration when welurch backward in the subway (orcar, bike etc) when it starts, orwhen it stops (lurch forward).
Note acceleration refers to : decreases in speed, increases in speed, and/or changes in direction i.e. to changes in the state of motion.
Newton’s 1
st
law says
then there must be a force acting (more next lecture)• Note also that acceleration has a direction
What is the acceleration of a cheetah that zips past yougoing at a constant velocity of 60 mph?
A) 0B) 60 mi/h
2
Not enough information given to answer problem
D) None of the above
Constant velocity means no changein velocity i.e. no acceleration
a)
A certain car goes from rest to 100 km/h in 10 s. What is itsacceleration?
10 km/h.s
(note units!)
b)
In 2 s, a car increases its speed from 60 km/h to 65 km/h while abicycle goes from rest to 5 km/h. Which undergoes the greateracceleration?The accelerations are the same, since they both gain 5 km/h in 2s, soacceleration = (change in v)/(time interval) = (5 km/h)/(2 s) = 2.5km/h.s
c)
What is the average speed of each vehicle in that 2 s interval, if weassume the acceleration is constant ?For car: 62.5 km/hFor bike: 2.5 km/h
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Free-fall: when falling object falls under influence ofgravity alone (no air resistance, nor any other restraint). How fast? During each second of fall, the object speeds up by about 10 m/s (independent of its weight)
Eg. Free-fall from restTime(s)
Velocity(m/s)
0
0
1
10
2
20
3
30
..
..
t^
10 t
Hence, free-fall
acceleration
= 10 m/s
(^2)
i.e. velocity gain of 10 meters per second,per second
Note! We rounded g to 10 m/s
2
We call this acc. due to gravity, in the table…
g
. Near surface of
Earth,
g
= 9.8 m/s
2
downwards.
So write
v = g t
if object dropped from rest
A ball is thrown up in the air. What is acceleration as itrises and falls?A)
g
= 9.8 m/s
2
downwards
g
= 9.8 m/s
2
upwards as it rises and
g
= 9.8 m/s
2
downwards as it falls
C) It starts out with a small acceleration that decreases as
it rises, then increases as it falls
D) None of the above
Answer: AThe acceleration due to gravity is
always
g = 9.8m/s
2
(near the surface of the
earth) and points towards earth. When ball is thrown up, its speed decreasesbecause acceleration (= rate of change of velocity) is in a direction opposite toits velocity. As it falls, it speeds up since acceleration is in the same directionas velocity.Don’t confuse velocity and acceleration!
How far? i.e. what distance is travelled?From the sketch before, we see distance fallen in equal time
intervals, increases as time goes on.
Actually, one can show (appendix in book), for any uniformly
accelerating object,distance travelled,
d
= ½ (acceleration x time x time)
So in free-fall :
d = ½ g t
2
Michael Jordan’s best hang-time was 0.9 s – this is thetime the feet are off the ground. Let’s round this to 1 s.How high can he jump?
Use d = ½ g t
2
. For 1 s hang-time, that’s ½ s up and ½ s
down. So, substitutingd = ½ (10) (1/2)
2
= 1.25 m
This is about 4 feet!Note that good athletes, dancers etc may appear to jump
higher, but very few can raise their
center of gravity
more
than 4 feet.
