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1. LAW OF ACCELERATION

2. LAW OF ACCELERATION
•Do you have any idea what is the other term
for the car’s gas pedal?
•Well, it is also known as the accelerator for
it controls the car’s acceleration.

3. LAW OF ACCELERATION
•Can you still recall what does acceleration
mean? You have learned that acceleration is
the rate at which the velocity is changing. A
change in velocity can mean any of the
following: (a) change in speed, (b) change in
direction, or (c) change in both speed and
direction.

4. LAW OF ACCELERATION
• Sir Isaac Newton found out that the acceleration of an
object is affected by two factors: force and mass.
Newton’s second law of motion which is otherwise
known as the law of acceleration, explains the
relationship among the following physical quantities:
acceleration, force, and mass.

5. Analyze and Discuss!
•Get to know what is stated in Newton’s second
law of motion by reading, analyzing and
answering the questions based on the given
situations.

6. Analyze and Discuss!
•Situation A: You are on a trip with your friends.
Then suddenly, the car stopped because it ran
out of gas. To avoid causing traffic, the car must
be pushed to the side of the road.

7. 1) When will the car move (accelerate) faster, when
only 1 person pushes it or when more persons push
it? Justify your answer.
2) What physical quantity was changed in this
situation?
3) What relationship exists between the varying
physical quantity and acceleration?

8. Analyze and Discuss!
•Situation B: Suppose you are biking one fine day.
You have seen that there is a pile of leaves in
front of you. Wind blows causing the pile of
leaves to spread.

9. 4) How would you compare the effect of a light
breeze of wind and a huge amount of wind on that
pile of leaves?
5) What physical quantity was varied in this
situation?
6) What relationship exists between the varying
physical quantity and acceleration?

10. Analyze and Discuss!
•Situation C: Two students are sitting on a
swing. Student A is 40 kilograms while
student B is 50 kilograms.

11. 7) Who will swing with greater acceleration: student A or
student B? Justify your answer.
8) What physical quantity was changed in this situation?
9) What relationship exists between the varying physical
quantity and acceleration?
10) Combining the ideas from the three situations, how do
you state the law of acceleration?

12. QUALITATIVE DESCRIPTION OF LAW OF
ACCELERATION
•Newton’s second law of acceleration states that,
“when a net force is acting on a body, the body
will accelerate in the direction of the force”.

13. QUALITATIVE DESCRIPTION OF LAW OF
ACCELERATION
•It states that, “the acceleration is directly
proportional to the net force acting on the body and
inversely proportional to the mass of the body”.
Similarly, it can be stated as, “the force applied on an
object is proportional to the mass of the object and
its acceleration”.

14. QUANTITATIVE DESCRIPTION OF LAW OF
ACCELERATION
• Mathematically, the law of acceleration can be expressed as:

15. QUANTITATIVE DESCRIPTION OF LAW OF
ACCELERATION
• From the equation, you can deduce that, the heavier
the object is, the greater force is needed to move it. In
addition, doubling the net force acting on an object
will also double the acceleration of the object.

16. QUANTITATIVE DESCRIPTION OF LAW OF
ACCELERATION
• Another important thing that you must remember
when dealing with equation of Newton’s second law is
that, it is a vector equation. This means that you will
be using it most of the time in component form, with
a separate equation for each component of force and
the corresponding component of acceleration:

17. QUANTITATIVE DESCRIPTION OF LAW OF
ACCELERATION
The above-given set of component equations is equivalent to
the single vector equation Σ𝐹⃗=𝑚𝑎⃗. Each component of the net
force equals the mass times the corresponding component of
acceleration (Young and Freedman, 2012).

18. QUANTITATIVE DESCRIPTION OF LAW OF
ACCELERATION
The following are the other salient points of Newton’s
second law of motion:
• the statement of Newton’s second law refers to external
forces which are the forces exerted on the body by other
bodies in its environment
• the equations are valid only when the mass is constant
• Newton’s second law is valid only in inertial frames of
reference.

19. QUANTITATIVE DESCRIPTION OF LAW OF
ACCELERATION
• Now, for you to have a clearer understanding of the quantitative
aspect of Newton’s law of acceleration, analyze and answer the
following sample problems.
1. worker applies a constant horizontal force with magnitude 37 N to a
box with mass 74 kg resting on a level floor with negligible friction.
What is the acceleration of the box?

20. Before you have the step-by step solution for this problem, you first
take note of the important things that you need to consider:
• For problems involving forces, it is important to choose first a
coordinate system and identify all the force acting on the object
being considered.
• It is really helpful to take one axis either along or opposite the
direction of the body’s acceleration.
+x – axis → horizontal axis that is to the right
-x – axis → horizontal axis that is to the left
+y – axis → vertical axis that is upward
-y – axis → vertical axis that is downward

22. •From figure 1, you can see that only the 37-N force
exerted by the worker has a nonzero x-component.
Hence,

23. •Rearranging the equation will give you the
following x-component of acceleration

24. •The acceleration is in the +x-direction, the
same direction as the net force. In this case,
the net force is constant, thereby the
acceleration is also constant.

25. 2) A 0.045-kg tennis ball approaches a racket
at 20 m/s. If it is in contact with the racket’s
string for 0.007 s, then rebounds at 20 m/s,
what is the average contact force between
the ball and racket?

28. The negative sign means that the force is in the direction
opposite to that of the ball when the ball approaches the
racket.

29. 3) A net horizontal force of 4750 N is applied
to a stalled car whose mass is 1250 kg. What
will be the car’s speed after 15 s?

33. Activity
1) A constant net force of 379 N is exerted to
accelerate a cart from rest to a velocity of 45
m/s in 15 s. What is the mass of the cart?

34. Activity
2) A 64.0-kg skater moving initially at 1.75
m/s on rough horizontal ice comes to rest
uniformly in 3.65 s due to friction from the
ice. What force does friction exert on the
skater?

35. Activity
3) A 16.0-kg box rests on a frozen pond,
which serves as a frictionless horizontal
surface. If a fisherman applies a horizontal
force with magnitude 48.0 N to the box, what
is the magnitude of acceleration produced?

36. Activity
4) An aircraft, P6 Cyanz, has a mass of 5.45 x
105 kg. The total force acting on its engine is
2.25 x 105 N. What is its acceleration?

37. Activity
5) A net horizontal force of 750 N is applied
to a stalled motorcycle whose mass is 181 kg.
What will be the motorcycle’s speed after 20
s?