3. KINEMATICS
? Describes motion in terms of
displacement, velocity, and acceleration.
Motion
? Is the displacement of an object in relation
to objects that are considered to be
stationary.
? It can also be defined as the continuous
change of position with respect to a certain
reference point.
4. DISTANCE AND DISPLACEMENT
Distance Vs. Displacement
Distance is a scalar quantity that refers to "how much ground an object
has covered" during its motion.
Displacement is a vector quantity that refers to "how far out of place an
object is"; it is the object's overall change in position.
¡÷
5. THE DIRECTION OF THE DISPLACEMENT VECTOR
In dealing with displacement, you need to consider its direction
which represents the direction from the initial position to the
final position. It is important to consider that displacement does
not depend on the path taken by an object but only on its initial
and final position.
6. THE DIRECTION OF THE DISPLACEMENT VECTOR
Calculate the displacement of a car as it moves from
position 1 towards position 2,
Answer: ¡÷x = xf - xi = -5 - 0 = -5
position 2 towards position 3,
Answer: ¡÷x = xf - xi = 5 - (-5) = 10
position 3 towards position 2.
Answer: ¡÷x = xf - xi = (-5) - (5) = -10
7. EXAMPLES
Example:
1. A car travels along a straight road 100 m east then 50 m
west. Find distance and displacement of the car.
2. A runner travels around rectangle track with length = 50
meters and width = 20 meters. After travels around rectangle
track two times, runner back to starting point. Determine
distance and displacement.
8. SPEED AND VELOCITY
Speed Vs. Velocity
Speed is a scalar quantity that refers to "how fast an object is
moving." Speed can be thought of as the rate at which an
object covers distance.
Where d= distance
t = time
9. SPEED AND VELOCITY
Speed Vs. Velocity
Velocity is a vector quantity that refers to "the rate at which an
object changes its position.¡°
10. SPEED AND VELOCITY
Example:
Jefrey walks 200 m from his house to school. Upon his arrival to
the gate of the school, he just realized that he needs to go to a
store which is halfway from his house to buy a pen. What are
his
a) average speed and b) average velocity when he arrived at the
store if the time it takes for the entire trip is 3 minutes?
15. INSTANTANEOUS SPEED AND VELOCITY
? Instantaneous speed is actually the
magnitude of the instantaneous velocity.
Given the value of the instantaneous
speed, you just add its direction then it
will now become the instantaneous
velocity of an object.
16. AVERAGE ACCELERATION
? Average acceleration is defined as the rate of change in
velocity over time.
? An object is accelerating if the change of its velocity is in
an increasing manner while an object is decelerating if
the change of its velocity is in a decreasing manner.
17. AVERAGE ACCELERATION
Accelerating motion of
an object
The car¡¯s initial velocity is
3.0 m/s. After 120s, the
velocity has changed to
7.0 m/s. Calculate the
average acceleration of
an object during the
given time interval.
18. AVERAGE ACCELERATION
Decelerating motion of an
object
The car¡¯s initial velocity is
15.0 m/s. After 120s, the
velocity has change to 2.0
m/s. Calculate the average
acceleration of an object
during the given time
interval.
22. THE BIG FOUR
Problem-Solving Strategy
1. Construct an informative diagram of the physical situation.
2. Identify and list the given information in variable form.
3. Identify and list the unknown information in variable form.
4. Identify and list the equation that will be used to determine
unknown information from known information.
5. Substitute known values into the equation and use appropriate
algebraic steps to solve for the unknown information.
6. Check your answer to insure that it is reasonable and
mathematically correct.
23. THE BIG FOUR
Problem-Solving
Example 1:
Ima Hurryin is approaching a stoplight moving with a velocity of
+30.0 m/s. The light turns yellow, and Ima applies the brakes and
skids to a stop. If Ima's acceleration is -8.00 m/s2
, then determine
the displacement of the car during the skidding process. (Note
that the direction of the velocity and the acceleration vectors are
denoted by a + and a - sign.)
26. THE BIG FOUR
Problem-Solving
Example 2:
Ben Rushin is waiting at a stoplight. When it finally turns
green, Ben accelerated from rest at a rate of a 6.00 m/s2
for a time of 4.10 seconds. Determine the displacement of
Ben's car during this time period.
30. THE BIG FOUR
Problem-Solving
Example 3:
A bike accelerates uniformly from rest to a speed of
7.10 m/s over a distance of 35.4 m. Determine the
acceleration of the bike.
34. THE BIG FOUR
Problem-Solving
Example 4:
A car traveling at 22.4 m/s skids to a stop in 2.55 s.
Determine the skidding distance of the car (assume
uniform acceleration).
39. FREE FALL
A free falling object is an object
that is falling under the sole
influence of gravity. Any object that
is being acted upon only by the
force of gravity is said to be in a
state of free fall.
42. FREE FALL
Important concepts to remember in Free Fall
1. An object in free fall experiences an acceleration of -9.8 m/s/s. Whether explicitly
stated or not, the value of the acceleration in the kinematic equations is -9.8 m/s2
for any freely falling object.
2. If an object is merely dropped (as opposed to being thrown) from an elevated
height, then the initial velocity of the object is 0 m/s.
3. If an object is projected upwards in a perfectly vertical direction, then it will slow
down as it rises upward. The instant at which it reaches the peak of its
trajectory, its velocity is 0 m/s.
4. If an object is projected upwards in a perfectly vertical direction, then the
velocity at which it is projected is equal in magnitude and opposite in sign to the
velocity that it has when it returns to the same height.
43. FREE FALL
EXAMPLE 1:
Luke Autbeloe drops a pile of
roof shingles from the top of
a roof located 8.52 meters
above the ground. Determine the
time required for the shingles to
reach the ground.
47. FREE FALL
EXAMPLE 2:
Rex Things throws his mother's
crystal vase vertically upwards
with an initial velocity of 26.2 m/s.
Determine the height to which the
vase will rise above its initial
height.
51. YOUR TURN
1. A car starts from rest and accelerates uniformly over a time of
5.21 seconds for a distance of 110 m. Determine the
acceleration of the car.
2. The observation deck of tall skyscraper 370 m above the
street. Determine the time required for a penny to free fall
from the deck to the street below.
52. YOUR TURN
1. A car starts from rest and accelerates uniformly over a time of 5.21
seconds for a distance of 110 m. Determine the acceleration of the car.
2. A plane has a takeoff speed of 88.3 m/s and requires 1365 m to reach
that speed. Determine the acceleration of the plane and the time
required to reach this speed.
3. The observation deck of tall skyscraper 370 m above the street.
Determine the time required for a penny to free fall from the deck to
the street below.
4. A baseball is popped straight up into the air and has a hang-time of
6.25 s. Determine the height to which the ball rises before it reaches its
peak. (Hint: the time to rise to the peak is one-half the total hang-
time.)
53. YOUR TURN
1. A baseball is popped straight up into the air and has a hang-time
of 6.25 s. Determine the height to which the ball rises before it
reaches its peak. (Hint: the time to rise to the peak is one-half
the total hang-time.)
2. A feather is dropped on the moon from a height of 1.40 meters.
The acceleration of gravity on the moon is 1.67 m/s2
. Determine
the time for the feather to fall to the surface of the moon.
3. An airplane accelerates down a runway at 3.20 m/s2
for 32.8 s
until is finally lifts off the ground. Determine the distance
traveled before takeoff.
4. A race car accelerates uniformly from 18.5 m/s to 46.1 m/s in
2.47 seconds. Determine the acceleration of the car and the
distance traveled.
#6: The negative value of displacement represents the direction of the change in position pointing towards the left of the x-axis while the positive displacement means direction pointing towards the right side of the x-axis.
#13: The average speed of the car following a path as shown in the Figure 3B below is 5 m/s. However, at an instant time of 3 minutes during its travel, its instantaneous speed is equal to 6 m/s. The car could have different instantaneous speeds during its travel or it might have a zero instantaneous speed if it stopped for a given time.
#39: Free-falling objects do not encounter air resistance.
All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s
Set example the leaning tower of Pisa
#40: Free-falling objects do not encounter air resistance.
All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s
Set example the leaning tower of Pisa
#41: Free-falling objects do not encounter air resistance.
All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s
Set example the leaning tower of Pisa
#42: Free-falling objects do not encounter air resistance.
All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s
Set example the leaning tower of Pisa
#43: Free-falling objects do not encounter air resistance.
All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s
Set example the leaning tower of Pisa
#47: Free-falling objects do not encounter air resistance.
All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s
Set example the leaning tower of Pisa
#51: Your hang time is the length of time that you¡¯re suspended in mid-air.
#52: Your hang time is the length of time that you¡¯re suspended in mid-air.
#53: Your hang time is the length of time that you¡¯re suspended in mid-air.
