An object is in Free-Fall when the only force acting on the object is the Force of Gravity, however, we haven’t defined Force much less the Force of Gravity, so, until we have defined the Force of Gravity, we have a slightly different definition. An object is in Free-Fall when: - It is not touching any other objects♥ - There is no air resistance (it’s in the vacuum we can breathe) We are now in the vacuum that we can breathe and will be for the remainder of this class, unless otherwise stated. Common Misconception: For some reason people think the word “fall” in Free-Fall means that the object must be going down. This is absolutely, not true. An object thrown upward is in Free-Fall from the moment it leaves the persons hand until it touches the ground.

1. PROJECTILE MOTION:
UAM(UNIFORMLY
ACCELERATED MOTION
AND FREE FALL)
FOURTH QUARTER- WEEK 1
PREPARED BY: ALVIN MARC M. DANCEL,LPT, MATBIO

2. RECALL:
• From your previous grade levels, you were able to quantify
non-uniform motion. In this module, you will describe the
horizontal and vertical dimensions of Uniformly Accelerated
Motion (UAM). These two dimensions of motion will be the
components of what we called, projectile motion. Before
proceeding to projectile motion as two-dimensional
motion, let’s have a review of motion in one dimension
involving the concepts of distance, displacement, speed,
velocity and acceleration.

3. 1. Distance
● It is the total length of the path traveled by an
object.
● The SI unit of distance is meter (m).
● Distance is always positive. It has no direction. It is an
example of a scalar.
2. Displacement
● It refers to the shortest distance between the object’s
two positions, like the distance between the object’s two
positions, like the distance between its point of origin and
its point of destination.

4. ● It is indicated by direction.
● The SI unit for displacement is meter (m).
● Displacement has a direction. It can be positive or
negative. It is an example of a vector.

6. 3.Speed
●Speed (v) is the distance (d)
covered by an object per unit time
(t). It is also the measure of how
fast an object travels. That is,
●Speed is scalar quantity

7. 4. Velocity
Velocity (v⃑) is the displacement (d⃑) covered by
an object per unit time (t). It is also the speed of an
object associated with a specific direction. That is,
Velocity is a vector quantity.

8. 5. Acceleration
Acceleration (a) is the change in velocity (∆v⃑) per unit time (t).
That is,There will only be acceleration when velocity changes.
The sign (+ or -) of acceleration indicates its direction.
Positive: North, East, up, right
Negative: West, South, down, left
Acceleration can be:
speeding up
slowing down
Turning

9. Consider a car on a road travel at a speed of 1 km per minute. After 3
minutes, there is no change in speed, therefore its speed is constant. The
car didn’t accelerate since its initial speed and final speed were the
This is referred to as uniform motion.
DistanceTime Speed
1 km 1 min1 km/min
2 km 2 min1 km/min
3 km 3 min1 km/min
Acceleration: 0 km/min2

10. Consider an airplane on a runway preparing for takeoff. Positions taken at equal time
intervals
Distance Time Speed
0.5 km1 min 0.5 km/min
2 km 2 min 1 km/min
12 km 3 min 4 km/min
are indicated in the figure below.
Acceleration: 2.67 km/min2
The change in an airplane’s position for each time interval is
shown in the figure above thus, it is moving faster and faster. This
that the plane is accelerating. This is referred to as uniform

11. You should bear in mind that:
Uniform motion is entirely different from uniform
acceleration. When a body travels equal distances in equal time
intervals or the velocity of the body does not change at all,
the body will be in uniform motion. Here acceleration is
When the velocity of the body changes at a constant rate
what is illustrated in the motion of the airplane, the body is said
to have uniform accelerated motion. Here acceleration is
constant as its velocity constantly changes over some time.

12. 𝒅 =
𝒗𝒊 + 𝒗𝒇
𝟐
𝒕
𝒗𝒇 = 𝒗𝒊 + 𝒂𝒕
𝒅 = 𝒗𝒊𝒕 +
𝟏
𝟐
𝒂𝒕𝟐
𝒗𝒇
𝟐 = 𝒗𝒊
𝟐 + 𝟐𝒂𝒅 𝒗𝒇𝒙 = 𝒗𝒐𝒙 + 𝟐𝒂𝒅𝒙
Where: Quantity Unit
displacement/distance (𝑑) meter (m)
time (t) second (s)
initial velocity/speed (𝑣𝑖) 𝑚𝑒𝑡𝑒𝑟
𝑠𝑒𝑐𝑜𝑛𝑑
(
𝑚
𝑠
)
final velocity/speed (𝑣𝑓) 𝑚𝑒𝑡𝑒𝑟
𝑠𝑒𝑐𝑜𝑛𝑑
(
𝑚
𝑠
)
acceleration (a) 𝑚𝑒𝑡𝑒𝑟
𝑠𝑒𝑐𝑜𝑛𝑑
𝑠𝑒𝑐𝑜𝑛𝑑
(
𝑚
𝑠2)

13. Sample Problems:
1. Araceraccelerates fromrestata constantrate of20
𝑚
𝑠2.
a.Howfastwillthe racerbegoing atthe end of6 s?
b.Howfarhas the racertraveled during this time?
Given: Unknown:
𝑣𝑖 = 0(the word fromrestappearin the sentence) a. 𝑣𝑓?
𝑎 = 20
𝑚
𝑠2 b.𝑑?
𝑡 = 6𝑠
Formula:
Sinceitisequaltozero,
initial velocity (vi) is
cancelledtosimplifythe
equation.
Sinceitisequaltozero,
initial velocity (vi) is
cancelledtosimplifythe
equation.

14. 𝑣𝑓 = 𝑣𝑖 + 𝑎𝑡 𝑑 =
𝑣𝑖 + 𝑣𝑓
2
𝑡
𝑣𝑓 = 𝑎𝑡 𝑑 =
𝑣𝑓
2
𝑡
Solution:
𝑣𝑓 = 𝑎𝑡 𝑑 =
𝑣𝑓
2
𝑡
𝑣𝑓 = 20
𝑚
𝑠2 6 𝑠 𝑑 =
120
𝑚
𝑠
2
6 𝑠
Answer:
a) 𝑣𝑓 = 120
𝑚
𝑠
𝑏) 𝑑 = 360 𝑚

15. 2. A car has an initial velocity of 40
𝑚
𝑠
and
stops over 120 m when the brakes are applied.
a. How long does it take for the car to stop?
b. What is the car’s deceleration?
Vf=0
d=120 m
vi=40 m/s
t=?
=?

16. 3. From rest, a car accelerated at 8 m/s2 for 10 seconds.
a) What is the position of the car at the end of the 10 seconds?
b) What is the velocity of the car at the end of the 10 seconds?
4. With an initial velocity of 20 m/s, a car accelerated at 8 m/s2 for 10
seconds.
a) What is the position of the car at the end of the 10 seconds?
b) What is the velocity of the car at the end of the 10 seconds?

17. FREE FALL -refers to the motion of a falling object or body
under the influence of gravity alone and no other forces with
the effects of air resistance considered negligible. Free
fall motion can be illustrated by the following:
a. object dropped
b. object thrown downward
c. object thrown upward

18. The following characterizes freefall motion:
● The negative sign indicates its downward direction. It
is approximately constant if the objects move over
distances not comparable to the earth’s radius.
● REMEMBER: The value of gravity (-9.8 m/s2) is not
dependent on the body’s mass. The mass and size
of the body or object in free fall don’t affect its velocity
and acceleration since its downward movement is
merely influenced by gravity.

19. The following characterizes freefall motion:
In this lesson, we neglect the effects of air
resistance to free falling objects, and the motion
of a body in vertical dimension is merely associated
with gravitational force.
● Since motion in freefall is accelerated, this means that
for every one (1) second, the velocity/speed of a
falling object increases by 9.8 m/s.
● At the highest point of its path, an object thrown
upward has zero (0) velocity and an acceleration
equal to g.

20. 𝑑 =
𝑣𝑖𝑦 + 𝑣𝑓𝑦
2
𝑡
𝑣𝑓𝑦 = 𝑣𝑖𝑦 + 𝑔𝑡
𝑑𝑦 = 𝑣𝑖𝑦𝑡 +
1
2
𝑔𝑡2
𝑣𝑓𝑦
2 = 𝑣𝑖𝑦
2 + 2𝑔𝑑𝑦
The subscript y means that the motion of objects in freefall is along the y-axis.
Where:
Quantity Unit
displacement/distance (d_y) meter (m)
time (t) second (s)
initial velocity/speed (v_iy) meter/second (m/s)
final velocity/speed (v_fy) meter/second (m/s)
acceleration due to gravity g=-9.8 m/s^2

21. 𝒅 =
𝒗𝒊 + 𝒗𝒇
𝟐
𝒕
𝒗𝒇 = 𝒗𝒊 + 𝒂𝒕
𝒅 = 𝒗𝒊𝒕 +
𝟏
𝟐
𝒂𝒕𝟐
𝒗𝒇
𝟐 = 𝒗𝒊
𝟐 + 𝟐𝒂𝒅 𝒗𝒇𝒙 = 𝒗𝒐𝒙 + 𝟐𝒂𝒅𝒙
Where: Quantity Unit
displacement/distance (𝑑) meter (m)
time (t) second (s)
initial velocity/speed (𝑣𝑖) 𝑚𝑒𝑡𝑒𝑟
𝑠𝑒𝑐𝑜𝑛𝑑
(
𝑚
𝑠
)
final velocity/speed (𝑣𝑓) 𝑚𝑒𝑡𝑒𝑟
𝑠𝑒𝑐𝑜𝑛𝑑
(
𝑚
𝑠
)
acceleration (a) 𝑚𝑒𝑡𝑒𝑟
𝑠𝑒𝑐𝑜𝑛𝑑
𝑠𝑒𝑐𝑜𝑛𝑑
(
𝑚
𝑠2)

22. 1. A small package is dropped from a bridge
15 m above a river. (Neglect the effects of air
resistance).
a. With what speed will it hit the water
below?
b. How long does it take the package to
reach the river?
Given:
g=-9.8 m/s^2
viy=0 (the object is dropped)
d=-15 m (negative is attached because the
object travels below the point of origin)

23. Unknown:
v_fy? b. t?
FORMULA:
〖v_fy〗^2= 〖v_iy〗^2+2gd_y
〖v_fy〗^2= 〖v_iy〗^2+2gd_y
±√(〖v_fy〗^2 )= ±√(2gd_y )
v_fy= ±√(2gd_y )
Solution:
v_fy= ±√(2gd_y )
v_fy= ±√(2(-9.8 m/s^2 )(-15 m) )
v_fy= ±√(294 m^2/s^2 )
v_fy= ±17.15 m/s
Answer:
v_fy= -17.15 m/s
Since the object is dropped, then the velocity must be negative. To solve for time:
v_fy=v_iy+gt
v_fy=gt
gt/g=v_fy/g
t=v_fy/g

24. . For an object thrown upward, then its final velocity 𝑣⃑𝑓𝑦 upon reaching its highest point is
equal to zero (0) (𝑣𝑓𝑦 = 0) and all quantities will be taken positive before reaching its highest
point. The total time in going up and moving down of an object thrown upward is equal to 𝑡𝑇 = 2𝑡.
d. 𝑔 = −9.8
𝑚
𝑠2 is always part of the given in freefall motion.
e. In extracting the root of a number, always bear in mind that there are two roots (a positive and
a negative), which one will be chosen depends on the situation in the problem.

25. 2. A BALL THROWN VERTICALLY
UPWARD REACHES ITS HIGHEST POINT
IN 4 SECONDS. FIND ITS INITIAL
VELOCITY.
GIVEN:
• g=-9.8ms2
• vfy=0 (the object is thrown upward)
• t=4s
• Unknown: viy
• FORMULA: vfy=viy+gt

26. THANK YOU AND
GOD BLESS!!!