By: Isaac Bonyah

Many students believe that deceleration is always negative. In fact, many textbooks define deceleration as: “negative of acceleration”. But is this really true? To answer this properly, we must first understand the concepts of velocity and change in velocity.

Understanding Velocity

Velocity is the rate of change of displacement with time. Unlike speed, velocity is a vector quantity, meaning it has:

· magnitude

· direction

The magnitude component of velocity is what we call speed.

What Does It Mean for Velocity to Change?

Since velocity is a vector quantity, a body can change its velocity in three different ways:

· Constant speed, changing direction: An example is a car moving around a curve at constant speed.

· Constant direction, changing speed: An example is a car speeding up or slowing down along a straight road.

· Changing speed and changing direction: An example is a car moving around a curve while also changing speed.

In all these situations, the body is changing its velocity.

What is acceleration?

Acceleration is the rate of change of velocity. Therefore, a body is accelerating whenever its velocity changes, through:

· change in speed; speeding up or slowing down.

· change in direction

· change in both speed and direction

Acceleration is also a vector quantity.

Acceleration and Straight-Line Motion

Consider a car moving eastward along a straight road.

Case 1: Constant Speed

If the car moves with a constant speed in a straight line:

· velocity remains constant

· acceleration is zero

This is because neither the speed nor direction changes.

Case 2: Speeding Up

If the car speeds up while moving eastward:

· velocity points eastward

· acceleration also points eastward

Thus, when a body speeds up, acceleration and velocity act in the same direction.

Case 3: Slowing Down

If the car slows down while moving eastward:

· velocity points eastward

· acceleration points westward

Thus, when a body slows down, acceleration acts opposite to the direction of velocity.

This opposing acceleration is what we call deceleration.

So, What Exactly Is Deceleration?

Deceleration is not a separate type of motion.

It is simply an acceleration that acts opposite to the direction of motion, causing the body to slow down. This means that deceleration depends on the relationship between:

· velocity direction

· acceleration direction

When Deceleration is Negative

Assume eastward is positive and westward is negative.

A body moving eastward and speeding up

Velocity is positive and acceleration is also positive.

Mathematical proof

A body moving eastward and slowing down

Velocity is positive but acceleration is westward. Therefore:

· velocity is positive

· acceleration is negative

In this case, deceleration is negative.

Mathematical proof

When Deceleration is Positive

Assume eastward is positive and westward is negative.

A body moving westward and speeding up

Velocity is negative and acceleration is also negative.

Mathematical proof

Here, we see that a negative acceleration does not always mean “deceleration’. It can also mean “acceleration” in the negative direction.

A body moving westward and slowing down

Velocity is negative but acceleration is eastward. Therefore:

· velocity is negative

· acceleration is positive

In this case, deceleration is positive.

Mathematical proof

Here, we see that deceleration is not always negative. It can also be positive if the body is slowing down in the negative direction.

Important Observation

A negative acceleration can mean:

· a body slowing down in the positive direction

· a body speeding up in the negative direction

A positive acceleration can mean:

· a body speeding up in the positive direction

· a body slowing down in the negative direction

This shows clearly that: The sign of the acceleration alone does not determine whether a body is speeding up or slowing down; the direction of motion is also another factor to consider.

Conclusion

Deceleration is not always negative. Deceleration simply means that acceleration acts opposite to the direction of motion, causing speed to decrease.

Whether the acceleration is positive or negative depends on the direction of motion, and whether the body is speeding up or slowing down. Therefore:

· negative acceleration is not always deceleration

· deceleration is not always negative

Physics students often encounter a familiar situation: a book resting quietly on a table. Most will confidently say:

· the weight of the book acts downward

· the normal force acts upward

· the two forces are equal and opposite

· therefore, they cancel each other due to Newton’s Third Law

This reasoning sounds correct, but it reveals a deep misunderstanding.

This article clarifies the concepts of weight, normal force and Newton’s Third Law, and addresses some of the most common misconceptions students hold.

What is Weight?

i. Weight is a gravitational force; specifically, it is the force of attraction exerted by the Earth on an object. It has the following characteristics:

ii. It acts vertically downward toward the Earth’s centre.

iii. It is a pulling force, not a pushing force.

iv. It exists whether or not the object is in contact with a surface.

What is Normal Force?

The normal force is a contact force that arises when two surfaces are in contact. It:

i. acts perpendicular to the surface of contact.

ii. is a pushing force exerted by one surface on another to prevent interpenetration.

iii. adjusts its magnitude depending on the situation, such as inclined surfaces, applied forces, acceleration, etc.

What does Newton’s Third Law mean?

Newton’s Third Law describes the interaction between two objects. It states that whenever two objects interact, each exert a force on the other. These forces have the following characteristics:

i. They are equal in magnitude.

ii. They are opposite in directions.

iii. They are of the same type or nature; both are either pushing forces or pulling forces.

These forces are known as action-reaction force pairs.

The Common Misconception

Consider a book resting on a table, as shown in the diagram below:

Two vertical forces act on the book:

· The weight of the book, which is the gravitational force exerted by the earth on the book, acting downward.

· The normal force, which is the upward contact force exerted by the table on the book:

Since the book is at rest, these forces are equal in magnitude but opposite in direction.

Many students conclude, “since the two forces are equal and opposite, they are action-reaction pair”. This is incorrect.

Why Weight and Normal Force are Not Action-Reaction pairs

Although these two forces are equal in magnitude and opposite in direction, they do not satisfy the conditions for a Newton’s Third Law action-reaction pair for the following reasons:

· They act on the same object. Both the weight and the normal force act on the book, whereas action-reaction forces must act on different objects. Because they act on the same object:

i. we can determine their resultant force. With the case above:

ii. In contrast, action-reaction force pairs cannot be combined to find a resultant, since they act on different objects.

· They are of different types. The weight is a gravitational or pulling or non-contact force, while the normal force is a contact or pushing force.

The Real Action-Reaction Pairs

To understand properly, we must identify the correct pairs:

· The reaction force to the normal force, which is the upward push by the table on the book, is the downward push of the book on the table. Both are contact forces, normal forces to be precise.

· The reaction force to the weight of the book, which is the earth downward pull on the book, is the upward pull of the book on the earth. Both are non-contact forces, gravitational forces to be precise.

Each pair:

· acts on different objects

· is of the same type

This is what Newton’s Third Law actually describe.

Another Common Error

Students often say: “The book exerts its weight on the table”. This is not accurate.

· The weight of the book is the earth’s gravitational force on the book, not a force exerted by the book on the table.

· This gravitational pull causes the book to press down on the table, producing a normal force. In other words, the force the book exerts on the table is a contact pushing force or normal force, not a pulling force or weight.

Is Normal Force Always Equal to Weight?

No. The normal force is not always equal to the weight of an object. This equality occurs only in specific situations.

Example: Elevator Motion

Consider a man of mass 50 kg standing on a weighing scale inside an elevator.

The forces acting on the man are:

i. the weight of the man

ii. the normal force exerted by the scale.

The scale measures the force the man exerts on it, which is equal in magnitude to the normal force, exerted by the scale on the man, according to Newton’s Third Law.

· When elevator moves with a constant velocity

The scale reads 500 N , equal to the man’s weight.

· When elevator accelerates upward with an acceleration of 2 meters per second square.

Scale reads 600 N, greater than the man’s weight.

· When elevator accelerates downward with an acceleration of 2 meters per second square.

The scale reads 400 N , less than the man’s weight.

Observations and Conclusion

i. the normal force is not always equal to the weight.

ii. the scale does not measure the man’s weight when the elevator accelerates. This demonstrates that the force exerted by the man on the scale is normal force, the reaction to the normal force exerted by scale on the man, and not weight.

iii. by convention, when the person is at rest or moving at constant velocity, the normal force equals weight, so the scale reading is taken as the person’s weight.

Application: Pressure Misconception

A common mistake is to calculate pressure using:

· This is only valid in special cases.

· In reality, pressure depends on the normal force, not weight.

Consider the examples below:

1. A block of mass 5 kg is pulled to the right on table by a force 60 N inclined at an angle of 30 degrees to the horizontal. What is the pressure exerted by the block on the table if the contact area of block is 5 square meters?

Misconception or incorrect approach

Why it is wrong:

This solution assumes that the block exerts its weight on the table. But the weight of the block is the earth’s force on block, not on table. The force the block exert on the table is a normal contact force, equal in magnitude to the normal force exerted by table on block.

The correct solution is:

This example shows that an object does not exert it weight on a surface.

2. A man of mass 50 kg stands in a lift accelerating upwards at 3 meters per second square. What is the magnitude of the force he exerts on the floor?

Misconception or incorrect approach

Force exerted on the floor = weight of man

Why it is wrong:

This solution assumes that the man exerts his weight on the floor of the lift. But the weight of the man is the earth’s force on the man, not the floor. The force the man exerts on the floor is a normal contact force, equal in magnitude to the normal force exerted by floor on the man.

The correct solution is:

This example again shows that an object does not exert it weight on a surface.

Conclusion

The confusion around weight, normal force, and Newton’s Third Law often comes from mixing two ideas:

· Balanced forces

· Action-reaction pairs

These are not the same.

· Forces that balance act on the same object.

· Action-reaction forces act on different objects.

Understanding this distinction clears up many errors in Mechanics.

Thank you for reading. Feel free to reach out via: 200002728@st.uew.edu.gh