2. Kinematics deals with the concepts that
are needed to describe motion.
Dynamics deals with the effect that forces
have on motion.
Together, kinematics and dynamics form
the branch of physics known as Mechanics.
3. 2.2 Speed and Velocity
Question 1: Explain the meaning of speed using your
own words.
21
18
10
0
5
10
15
20
25
Incorrect Partially correct Incorrect
20 20 20
0
5
10
15
20
25
Correct Partially Incorrect
4. 2.2 Speed and Velocity
Question 2: Is the 257 km/h he was caught driving
an average or instantaneous speed?
.
11
39
0
5
10
15
20
25
30
35
40
45
Average Instantaneous
50
10
0
10
20
30
40
50
60
Instantaneous Average
5. 2.2 Speed and Velocity
Question 4: Do you think that speed kills?
32
3
15
0
5
10
15
20
25
30
35
It Kills It Does'nt It Depends
31
8
21
0
5
10
15
20
25
30
35
Kills It does nt It depends
Series1
7. 2.2 Average Speed and Velocity
Average speed is the total distance traveled divided by the time
required to cover the distance.
timeTotal
DistanceTotal
speedAverage
SI units for speed: meters per second (m/s)
Mathematically it means
Note: The emphasis of on the total distance covered
divided total time taken
8. 2.2 Speed and Velocity
Exercise: Distance Run by a Jogger
How far does a jogger run in 1.5 hours (5400 s) if his
average speed is 2.22 m/s?
timeElapsed
Distance
speedAverage
m12000
s540022.2
timeElapsedspeedAverageDistance
s
m
9. 2.2 Speed and Velocity
Average velocity is the displacement divided by the elapsed
time.
timeElapsed
ntDisplaceme
velocityAverage
ttt o
o xxx
v
Note: The emphasis of on the displacement divided
change in time
10. 2.2 Speed and Velocity
Exercise: The World’s Fastest Jet-Engine Car
Andy Green in the car set a world record of 341.1 m/s in 1997. To
establish such a record, the driver makes two runs through the
course, one in each direction to nullify wind effects. From the
data, determine the average velocity for each run.
11. 2.2 Speed and Velocity
sm5.339
s4.740
m1609
t
x
v
sm7.342
s4.695
m1609
t
x
v
12. 2.2 Instantaneous Speed and Velocity
The instantaneous velocity indicates how often
an object changes position and the direction
of motion at each
instant of time.
tt
x
v
0
lim
13. Speed versus Velocity
• Speed is associated with distance while
velocity is associated with displacement
• Change in velocity means that:
1)The magnitude of velocity changes or/and
2)The direction of an object changes
• If motion is in one dimension, the
magnitude and direction of speed is the
same as that of velocity, that’s why they
can be used interchangeably
14. 2.3 Acceleration
The notion of acceleration emerges when a change in
velocity is combined with the time during which the
change occurs.
Acceleration measures how often the velocity
changes with respect to time.
The average acceleration is then given by:
ttt o
o vvv
a
15. 2.3 Acceleration
Example 3 Acceleration and Increasing Velocity
Determine the average acceleration of the plane.
sm0ov
hkm260v
s0ot s29t
s
hkm
0.9
s0s29
hkm0hkm260
o
o
tt
vv
a
19. For you to do
At one instant of time, a car and a truck are traveling side by
side in adjacent lanes of a highway. The car has a greater
velocity than the truck has. Does the car necessarily have
the greater acceleration?
A. Yes
B. No
Explanation
20. Two cars are moving in the same direction (the positive
direction) on a straight road. The acceleration of each car
also points in the positive direction. Car 1 has a greater
acceleration than car 2 has. Which one of the following
statements is true?
A. The velocity of car 1 is always greater than the velocity of car 2.
B. The velocity of car 2 is always greater than the velocity of car 1.
C. In the same time interval, the velocity of car 1 changes by a greater
amount than the velocity of car 2 does.
D. In the same time interval, the velocity of car 2 changes by a greater
amount than the velocity of car 1 does.
21. 2.4 Equations of Kinematics for Constant Acceleration
It is customary to dispense with the use of boldface symbols
overdrawn with arrows for the displacement, velocity, and
acceleration vectors. We will, however, continue to convey
the directions with a plus or minus sign.
o
o
tt
vv
a
o
o
tt
xx
v
o
o
tt
xx
v
o
o
tt
vv
a
22. Your Turn
A car is traveling along a straight road and is decelerating.
Which one of the following statements correctly describes
the car’s acceleration?
(a) It must be positive.
(b) It must be negative.
(c) It could be positive or negative.
Answers (a) and (b) are incorrect.
The term “decelerating” means only that the acceleration vector points opposite to the velocity vector.
It is not specified whether the velocity vector of the car points in the positive or negative direction.
Therefore, it is not possible to know whether the acceleration is positive or negative.
Answer (c) is correct.
The acceleration vector of the car could point in the positive or the negative direction, so that
the acceleration could be either positive or negative, depending on the direction in which the car
is moving.
23. Your Turn
When an object moves with constant acceleration, its
velocity…
A: Increases
B: Decreases
C: remains constant
D: Both A and B can be correct
24. 2.4 Equations of Kinematics for Constant Acceleration
o
o
tt
xx
v
0ox 0ot
tvvtvx o2
1
Let the object be at the origin when the clock starts.
t
x
v
25. 2.4 Equations of Kinematics for Constant Acceleration
o
o
tt
vv
a
t
vv
a o
ovvat
atvv o
26. 2.4 Equations of Kinematics for Constant Acceleration
atvv o
tatvvtvvx ooo 2
1
2
1
2
2
1
attvx o
27. 2.4 Equations of Kinematics for Constant Acceleration
a
vv
vvtvvx o
oo 2
1
2
1
t
vv
a o
a
vv
t o
a
vv
x o
2
22
28. 2.4 Equations of Kinematics for Constant Acceleration
Equations of Kinematics for Constant Acceleration
tvvx ox 2
1
0
2
2
1
0
)( attvx ox
atvv o
)(2 0
22
xxavv o
29. 2.5 Applications of the Equations of Kinematics
Reasoning Strategy
1. Make a drawing.
2. Decide which directions are to be called positive (+) and
negative (-).
3. Write down the values that are given for any of the five
kinematic variables.
4. Select the appropriate equation.
5. When the motion is divided into segments, remember that
the final velocity of one segment is the initial velocity for the next.
6. Keep in mind that there may be two possible answers to a
kinematics problem.
30. 2.4 Equations of Kinematics for Constant Acceleration
m110
s0.8sm0.2s0.8sm0.6
22
2
1
2
2
1
attvx o
31. 2.4 Equations of Kinematics for Constant Acceleration
Example 6 Catapulting a Jet: Find its displacement.
sm0ov ??x2
sm31a sm62v
m62
sm312
sm0sm62
2 2
2222
a
vv
x o
32. 2.5 Applications of the Equations of Kinematics
Activity: Physics and the Construction Industry
You are designing an airport for small planes. One kind of the
plane that might use the airfield must reach a speed before a
takeoff of at least 27.8 m/s. and can accelerate at a 2.00 m/s2.
(a) If the runway is 150m long, do you think the airplane can
reach the required speed for takeoff? (b) If not, what minimum
length must the runway have?
x a v vo t
150 m 2 m/s2 ? 27.8 m/s
33. A ball is thrown vertically upwards from the surface of the earth.
Consider the following quantities based on the motion of the ball.
(1) Speed; (2) velocity; (3) acceleration
Question 1 : Speed, velocity and acceleration
1.1 Which of these is (are) zero when the ball has reached the maximum
height at point C? Give reasons for your answer.
A: 1 and 2 only, B: 1 and 3 only, C: 1 only, D: 2 only, E: 1, 2 and 3
Reason:
1.2 What do you think will be the magnitude and direction of acceleration of
an object at the following points? Say : Increase , decrease and remain
constant , for direction down is positive up negative Give reasons for your
answer.
1.2.1 A 1.2.2 B 1.2.3 C 1.2.4 D 1.2.5 E
1.3 What do you think will happen to the velocities of an object at the
following points? (Only say, increase, decrease, zero or remains the same
and give reasons)
1.3.1 A 1.3.2 B 1.3.3 C 1.3.4 D 1.3.5 E
Reason:
34. Question 2: The case of two objects with
different masses
If two objects, one with BIGGER mass and the other
with SMALLER mass are made to fall from the same
height, Which one do you think it will reach the ground
first?
A: Object with bigger mass
B: Object with smaller mass
C: They will reach the ground at the same
Explanation
35. Question 3
Does the pellet in part b strike the ground beneath the cliff
with a smaller, greater, or the same speed as the pellet
in part a?
36. 2.6 Freely Falling Bodies
Generally, during the absence of air resistance, it is found
that all bodiesat the same location above the Earth fall
vertically with the same acceleration.
If the distance of the fall is small compared to the radius of
the Earth, then the acceleration remains essentially
constant throughout the descent.
This idealized motion is called free-fall and the acceleration
of a freely falling body is called the acceleration due to
gravity.
sm80.9 2
g
37. 2.4 Equations of Kinematics for Constant Acceleration
Equations of Kinematics for Constant Acceleration
tvvx ox 2
1
0
2
2
1
0
)( attvx ox
atvv o
)(2 0
22
xxavv o
38. 2.4 Equations of Kinematics for Constant Acceleration
Equations of Kinematics for Constant Acceleration
tvvy oy 2
1
0
2
2
1
0
)( gttvy oy
gtvv o
)(2
0
22
yygvv o
41. About the MCQ Test
2
7
14
21
13
2
4
0
5
10
15
20
25
0 to 4 5 to 7 8 to 9 10 to 11 12 to14 15 to 16 17 and above
ActualNumberofStudents
PS1AFET Test 1 Scores Distribution 2013
Only 30% which is 19 out of 63 passed
42. 2.6 Freely Falling Bodies
A Falling Stone:
A stone is dropped from the top of a tall building. After 3.00s
of free fall, what is the displacement y of the stone?
Let the downwards
motion be positive
y g v vo t
? 9.80
m/s2
0
m/s
3.0 s
m1.44
s00.3sm80.9s00.3sm0
22
2
1
2
2
1
0
gttvy oy
43. 2.6 Freely Falling Bodies
How High Does it Go?
The referee tosses the coin up
with an initial speed of 5.00m/s.
In the absence if air resistance,
how high does the coin go above
its point of release?
y g v vo t
? -9.80 m/s2 0 m/s +5.00
m/s
44. 2.6 Freely Falling Bodies
)(222
yoo ygvv
g
vv
yy o
2
22
0
m28.1
sm80.92
sm00.5sm0
2 2
2222
0
g
vv
yy o
45. 2.6 Freely Falling Bodies
Conceptual Example 14 Acceleration Versus Velocity
There are three parts to the motion of the coin. On the way
up, the coin has a vector velocity that is directed upward and
has decreasing magnitude. At the top of its path, the coin
momentarily has zero velocity. On the way down, the coin
has downward-pointing velocity with an increasing magnitude.
In the absence of air resistance, does the acceleration of the
coin, like the velocity, change from one part to another?
46. Test your Knowledge
1. A sandbag is dropped from a height of 150 m, from a hot air
balloon that is moving upwards with a velocity of 5.0 ms-1. Ignore
air resistance.
a) What is the initial velocity of the sandbag?
b) How long will the bag take to reach the ground?
2. A bicycle’s brakes can produce a deceleration of 2.5 ms-2. How far
will the bicycle travel before stopping, if it is moving at 10 ms-1
when the brakes are applied?
3. Starting from a dead stop at the bottom of the on-ramp it can be
assumed that John accelerates at a rate of 6.7 m/s2. How long does
it take for John to reach a speed of 30m/s? How far has John
travelled in this time if you take his starting point to be 0m?
4. Baseball pitcher Josh Beckett throws a ball straight up in the air, the
balls mass is 4kg, and he releases it at a speed of 35m/s, what is
the maximum height that the ball will reach, and how long will it take
for the ball to come back down and hit the ground next to him?
Assume there is no air resistance, and the ball is released from and
returns to a level of 0m.
Prescribed book Ch 2 no 9 to 11; 28, 34, 41, 57 & 62
