Types of Velocity, Average Velocity, Uniform and Non-Uniform Velocity, Instantaneous Velocity, Examples

ANAND CLASSES study material and notes to learn about types of velocity, including uniform velocity, non-uniform velocity, average velocity, and instantaneous velocity with formulas, examples, MCQs, FAQs, worksheets, and test papers for JEE, NEET, and CBSE Class 11 exams.

Velocity helps us analyze how fast an object is moving and in which direction. Unlike speed, which only measures magnitude, velocity is a vector quantity, meaning it has both magnitude and direction.

Types of Velocity

1. Uniform Velocity

• An object is said to have uniform velocity if it covers equal displacements in equal time intervals without changing direction.
• The magnitude and direction remain constant throughout the motion.
• Example: A car moving at a constant speed of 60 km/h on a straight highway has uniform velocity.
• Mathematical Representation: $$v = \frac{\text{Displacement (Δx)}}{\text{Time (Δt)}}$$ where v is the velocity, Δx is the displacement, and Δt is the time interval.

2. Non-Uniform Velocity

• When an object covers unequal displacements in equal intervals of time, it is said to have non-uniform velocity.
• This means either the speed, direction, or both change during the motion.
• Example: A car moving in city traffic, where it speeds up and slows down frequently.
• Graphical Representation: The velocity-time graph of non-uniform velocity is not a straight line.

3. Average Velocity

• It is defined as the total displacement divided by the total time taken.
• Formula: $$v_{avg} = \frac{\text{Total Displacement}}{\text{Total Time}}$$
• Example: If a car moves 50 km east and then 30 km west in 2 hours, the average velocity is: $$v_{avg} = \frac{(50-30)\text{ km}}{2 \text{ hr}} = 10 \text{ km/hr east}$$
• Note: If the total displacement is zero, the average velocity is zero.

4. Instantaneous Velocity

• The velocity of an object at a specific instant of time.
• It is mathematically given by the derivative of displacement with respect to time: $$v = \lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t}$$
• Example: The speedometer reading of a car at a particular instant shows the instantaneous velocity.
• Graphically: The slope of the displacement-time graph gives the instantaneous velocity.

Question-Answer Format for Exams (JEE, NEET, CBSE Class 11)

Q1. Define velocity. How is it different from speed?
Ans: Velocity is the rate of change of displacement with time. It is different from speed because velocity is a vector quantity (has direction), whereas speed is a scalar quantity (has only magnitude).

Q2. What is the SI unit of velocity?
Ans: The SI unit of velocity is meters per second (m/s).

Q3. How can we calculate average velocity if the velocity is changing?
Ans: If velocity is changing, we use the formula:$$v_{avg} = \frac{x_2 – x_1}{t_2 – t_1}$$ where $x_1, x_2$ are initial and final positions, and $t_1, t_2$ are initial and final times.

FAQs

Q1: Can velocity be negative?
Ans: Yes, velocity can be negative when an object moves in the opposite direction to the chosen reference direction.

Q2: Is it possible to have zero velocity but non-zero acceleration?
Ans: Yes, when an object changes direction (like at the highest point of projectile motion), its velocity can be zero at that instant, but acceleration remains.

MCQs with Answers and Explanations

Q1. A body is moving with uniform velocity. What will be its acceleration?
A) Positive
B) Negative
C) Zero
D) Variable

Answer: C) Zero
Explanation: If velocity is uniform, there is no change in velocity, hence acceleration is zero.

Q2. A car moves 40 km north and then 30 km south in 2 hours. What is its average velocity?
A) 5 km/h
B) 10 km/h
C) 15 km/h
D) 20 km/h

Answer: B) 10 km/h
Explanation: The net displacement is 40 – 30 = 10 km north, and time is 2 hours, so average velocity is 10/2 = 5 km/h north.

Do You Know?

• Velocity-time graphs help in finding acceleration and displacement.
• A geostationary satellite has a uniform velocity as it moves at a constant speed around Earth.
• Light waves travel at different velocities in different mediums.

Worksheet

1. Define uniform and non-uniform velocity with examples.
2. Derive the equation for average velocity.
3. A bike moves with a velocity of 5 m/s and accelerates to 15 m/s in 5 seconds. Find the acceleration.

Test Paper (Total: 20 Marks)

Section A (1 Mark Each)

1. Define velocity.
2. What is the SI unit of velocity?

Section B (2 Marks Each)

3. Differentiate between speed and velocity.
4. Give an example of instantaneous velocity.

Section C (3 Marks Each)

5. A car moves 80 km north and then 20 km south in 4 hours. Calculate its average velocity.
6. Explain how velocity is different from acceleration.

Section D (5 Marks Each)

7. Explain uniform and non-uniform velocity with velocity-time graph.

Important Points for Quick Revision

• Velocity = Displacement/Time.
• Uniform velocity: No change in speed or direction.
• Non-uniform velocity: Change in speed or direction.
• Average velocity: Total displacement/Total time.
• Instantaneous velocity: Velocity at a specific instant.

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