2.3.2 (C) Uniform and Variable Velocity

Just as speed can be constant or changing, velocity can also be constant or changing. However, because velocity is a vector (having both magnitude and direction), the conditions for uniform velocity are stricter than for uniform speed. An object can have a constant speed but still have a variable velocity if its direction of motion is changing. Understanding this distinction is crucial for analyzing motion correctly.

Definition

Uniform Velocity: If an object covers equal displacements in equal intervals of time, we say that the object is moving with uniform velocity. Uniform velocity means the velocity does not change—neither its magnitude (speed) nor its direction.

Variable Velocity: If an object's velocity changes over time, it is said to be moving with variable velocity. A change in velocity can occur if the speed changes, the direction changes, or both change.

Main Idea

The main idea is that uniform velocity requires both constant speed and constant direction. This is a more restrictive condition than uniform speed, which only requires constant speed. For example, a car moving at a constant 60 km/h on a straight road has uniform velocity. But a car moving at a constant 60 km/h around a circular track has variable velocity, because its direction is constantly changing. Variable velocity is the more common situation in real life.

Core Concept

• The speed is constant.
• The direction is constant.

Example: A car moving on a straight highway with the cruise control set to 80 km/h is an example of uniform velocity. It covers 80 km in every hour, and it is always moving in the same direction.

• Speed changes: The object accelerates or decelerates (e.g., a car in city traffic).
• Direction changes: The object moves in a curved path (e.g., a car going around a bend, a satellite in orbit).
• Both change: The object's speed and direction both change (e.g., a car on a winding mountain road).

The Satellite Example The text provides an excellent example: "A satellite moving with a constant speed in a circular orbit around Earth does not have a constant velocity since its direction of movement is constantly changing as shown in figure 2.9."

This is a crucial point. The satellite's speed is constant, but its velocity is variable because its direction is continuously changing. This example clearly illustrates the difference between speed (scalar) and velocity (vector).

Detailed Explanation

The distinction between uniform and variable velocity is fundamental in physics.

• Friction and air resistance cause objects to slow down.
• The path of motion is rarely perfectly straight.

However, for many physics problems, we assume uniform velocity to simplify calculations. When velocity is uniform, the instantaneous velocity is equal to the average velocity for any time interval.

Variable Velocity Variable velocity is the norm in real life. Objects speed up, slow down, and change direction. The text states: "To produce variable velocity, either the speed or the direction is changed (or both are changed)." This is why the concept of acceleration (the rate of change of velocity) is so important—it describes how velocity changes.

The Key Difference The key difference between uniform and variable velocity is that uniform velocity requires both constant speed and constant direction. Variable velocity occurs if either the speed or the direction changes.

Intermediate Level

In physics, velocity is a vector, which means it has both magnitude and direction. Uniform velocity means neither the magnitude nor the direction changes. This is a stricter condition than uniform speed, which only requires the magnitude to be constant. For example, a car moving at a constant 60 km/h on a straight road has uniform velocity. But a car moving at a constant 60 km/h around a circular track has uniform speed but variable velocity, because its direction is continuously changing. This distinction is important for understanding acceleration, which is the rate of change of velocity. An object with variable velocity is accelerating, even if its speed is constant (as in circular motion). This is why the satellite example is so important—it shows that acceleration can occur without a change in speed.

Important Points

• - Uniform velocity: Equal displacements in equal intervals of time. Speed and direction are both constant.
• - Variable velocity: Velocity changes. This can be due to a change in speed, a change in direction, or both.
• - Uniform velocity requires constant direction, which is a stricter condition than uniform speed.
• - An object moving in a circle at constant speed has variable velocity because its direction is changing.
• - Acceleration is the rate of change of velocity, so any object with variable velocity is accelerating.

Remember

• - Uniform Velocity: Constant speed + constant direction.
• - Variable Velocity: Changing speed, changing direction, or both.
• - Key Example: Satellite in circular orbit has uniform speed but variable velocity.
• - Acceleration: Occurs whenever velocity is variable (even if speed is constant).

Common Mistakes

• - Confusing uniform velocity with uniform speed: Uniform velocity requires both constant speed and constant direction. Uniform speed only requires constant speed.
• - Thinking constant speed means constant velocity: An object moving in a circle at constant speed has a changing velocity because its direction is changing.
• - Forgetting that velocity is a vector: Velocity has both magnitude and direction. A change in either one means the velocity is variable.

Quick Revision

Uniform velocity occurs when an object covers equal displacements in equal intervals of time, meaning both its speed and direction are constant. Variable velocity occurs when the velocity changes, which can happen if the speed changes, the direction changes, or both. A satellite moving at a constant speed in a circular orbit has variable velocity because its direction is continuously changing.

60-Second Revision

• Key Example: Satellite in orbit has uniform speed but variable velocity (direction changes).
• Acceleration: Any change in velocity (even just direction) means acceleration.
• Remember: Velocity is a vector, so direction matters!

Frequently Asked Questions (FAQs)

Q1. What is uniform velocity? Answer: Uniform velocity is when an object covers equal displacements in equal intervals of time. This means both the speed and the direction of motion are constant.

• Q2. What is variable velocity?
• Answer: Variable velocity is when an object's velocity changes over time. This can happen if the speed changes, the direction changes, or both change.

Q3. What is the difference between uniform velocity and uniform speed? Answer: Uniform velocity requires both constant speed and constant direction. Uniform speed only requires constant speed. An object can have uniform speed but variable velocity if its direction is changing (e.g., circular motion).

Q4. Why does a satellite in a circular orbit have variable velocity? Answer: A satellite in a circular orbit has a constant speed, but its direction of motion is continuously changing as it goes around the Earth. Since velocity is a vector (magnitude and direction), a change in direction means the velocity is changing (variable).

• Q5. Can an object have a constant velocity but a changing speed?
• Answer: No. If the velocity is constant, both the speed and direction are constant. If the speed changes, the velocity changes.

Q6. How is variable velocity related to acceleration? Answer: Acceleration is the rate of change of velocity. Any object with variable velocity is accelerating, even if its speed is constant (as in circular motion).

Q7. Give an example of an object with uniform velocity. Answer: A car moving on a straight highway with the cruise control set to a constant speed (e.g., 80 km/h) is an example of uniform velocity. It moves at a constant speed in a constant direction.

Multiple Choice Questions (MCQs)

• Q1. If an object covers equal displacements in equal intervals of time, it is moving with:
• A. Variable velocity
• B. Uniform velocity
• C. Average velocity
• D. Instantaneous velocity

• Correct Answer: B
• Explanation: The text defines uniform velocity as covering equal displacements in equal intervals of time.

• Q2. Uniform velocity requires:
• A. Only constant speed
• B. Only constant direction
• C. Both constant speed and constant direction
• D. Neither constant speed nor constant direction

• Correct Answer: C
• Explanation: Uniform velocity means the velocity does not change, which requires both the speed and direction to be constant.

• Q3. A satellite moving at a constant speed in a circular orbit has:
• A. Uniform velocity
• B. Variable velocity
• C. Zero velocity
• D. Infinite velocity

• Correct Answer: B
• Explanation: The text states that the satellite does not have constant velocity because its direction of movement is constantly changing.

• Q4. Variable velocity occurs when:
• A. The speed changes
• B. The direction changes
• C. Both speed and direction change
• D. Any of the above

• Correct Answer: D
• Explanation: The text states that to produce variable velocity, either the speed or the direction is changed (or both are changed).

• Q5. Which of the following is an example of uniform velocity?
• A. A car accelerating from rest
• B. A car moving at a constant speed on a straight road
• C. A car going around a bend
• D. A satellite in a circular orbit

• Correct Answer: B
• Explanation: A car moving at a constant speed on a straight road has both constant speed and constant direction, which is uniform velocity.

• Q6. A car moving at a constant speed around a circular track has:
• A. Uniform velocity
• B. Variable velocity
• C. Zero velocity
• D. Constant velocity

• Correct Answer: B
• Explanation: The direction of motion is continuously changing, so the velocity is variable.

• Q7. Which of the following is NOT a characteristic of variable velocity?
• A. Speed changes
• B. Direction changes
• C. Velocity remains constant
• D. Both speed and direction change

• Correct Answer: C
• Explanation: Variable velocity means the velocity is changing, so it does not remain constant.

• Q8. The text uses the example of a satellite to explain:
• A. Uniform speed
• B. Variable velocity
• C. Average speed
• D. Instantaneous speed

• Correct Answer: B
• Explanation: The text uses the satellite example to show that an object can have constant speed but variable velocity because its direction is changing.

• Q9. If a car is moving at a constant 60 km/h on a straight road, its velocity is:
• A. Variable
• B. Uniform
• C. Zero
• D. Infinite

• Correct Answer: B
• Explanation: The car has constant speed and constant direction, so its velocity is uniform.

• Q10. Acceleration occurs when:
• A. Speed is constant
• B. Direction is constant
• C. Velocity is variable
• D. Velocity is uniform

Correct Answer: C Explanation: Acceleration is the rate of change of velocity. It occurs whenever velocity changes (becomes variable), whether due to a change in speed, direction, or both.

Frequently Asked Questions (FAQs)

Q1. Can an object have uniform speed but variable velocity? Answer: Yes. A satellite in a circular orbit has uniform speed (constant magnitude) but variable velocity (changing direction). This is because velocity is a vector, and a change in direction is a change in velocity.

Q2. What is the difference between uniform speed and uniform velocity? Answer: Uniform speed only requires constant speed. Uniform velocity requires both constant speed and constant direction. An object can have uniform speed but variable velocity if its direction changes.

• Q3. Can an object have variable speed but uniform velocity?
• Answer: No. If the speed is changing, the velocity is changing, so it cannot be uniform.

• Q4. Is it possible to have uniform velocity in a curved path?
• Answer: No. In a curved path, the direction of motion is continuously changing, so the velocity cannot be uniform.

• Q5. How is uniform velocity related to acceleration?
• Answer: If an object has uniform velocity, its acceleration is zero (since velocity is not changing). If an object has variable velocity, it is accelerating.

Q6. Give an example of an object with variable velocity due to a change in speed. Answer: A car accelerating from a red light has variable velocity because its speed is increasing. A car braking to a stop also has variable velocity because its speed is decreasing.

• Q7. Give an example of an object with variable velocity due to a change in direction.
• Answer: A car going around a circular track at a constant speed has variable velocity because its direction is continuously changing.

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