Velocity Definition, Formula, Types, Difference Between Speed & Velocity, Uniform & Non Uniform Velocity

Velocity is a fundamental concept in physics that describes the motion of an object in a specific direction. Unlike speed, which only tells us how fast an object is moving, velocity also includes information about the direction of movement.

Definition of Velocity

Velocity of a body is the displacement per unit time in a specified direction.

Mathematically,

$$\text{Velocity} (v) = \frac{\text{Displacement}}{\text{Time taken}}$$

Alternatively, since displacement is the distance traveled in a specified direction: $$v = \frac{s}{t}$$ where:

• $v$ = velocity of the body
• $s$ = displacement of the body (measured in meters in SI units)
• $t$ = time taken for the displacement (measured in seconds in SI units)

Velocity is a vector quantity because it has both magnitude and direction. Its SI unit is meters per second (m/s or m s⁻¹) and CGS unit is (cm/s or cm s⁻¹)

Dimensions of Velocity = [M⁰L¹T^–1].

Difference Between Speed and Velocity

Speed and velocity are often confused because they are similar, but they have key differences:

Thus, velocity provides more information than speed because it tells us both how fast something is moving and in which direction.

Types of Velocity

1. Uniform Velocity (Constant Velocity)

A body has uniform velocity if it travels equal distances in equal intervals of time in a straight line.

Conditions for Uniform Velocity:

✔ The body must move in a straight line.

✔ It must cover equal distances in equal time intervals.

✔ Its direction must remain unchanged.

Example: A car moving at 40 km/hr due North without changing speed or direction.

2. Non-Uniform Velocity (Variable Velocity)

Velocity changes when:

• The speed of the object changes.
• The direction of the object changes.
• Both speed and direction change.

Example:

• A car moving in a zig-zag path at varying speeds has non-uniform velocity.
• A car moving in a circular path at constant speed has non-uniform velocity because its direction changes continuously.

Key Formulas

1. $v = \frac{s}{t}$ (Velocity formula)
2. $s = v \times t $(Distance formula)
3. $v_{avg} = \frac{\text{Total Displacement}}{\text{Total Time}} $(Average velocity)

These formulas are useful for solving numerical problems related to motion.

Conceptual Questions with Answers

Q1: Can the speed of an object be constant but its velocity variable?

Answer: Yes, when an object moves in a circular path at constant speed, its direction changes continuously, making its velocity variable.

Q2: Can the average velocity of a moving object be zero?

Answer: Yes, if an object moves in one direction and then returns to its starting point, the displacement is zero, making the average velocity zero.

Q3: Is it possible for velocity and speed to be numerically equal?

Answer: Yes, if an object moves in a straight line without changing direction, then the magnitude of its speed and velocity will be the same.

Multiple Choice Questions (MCQs)

Q1: Velocity is a ______ quantity.

• (a) Scalar
• (b) Vector
• (c) Neutral
• (d) None of the above
  Answer: (b) Vector
  Explanation: Velocity has both magnitude and direction.

Q2: If a car moves 100 m East and then 100 m West in 10 sec, what is its average velocity?

• (a) 20 m/s
• (b) 10 m/s
• (c) 0 m/s
• (d) 5 m/s

Answer: (c) 0 m/s Explanation: Since displacement is zero, velocity is also zero.

Do You Know?

✔ Velocity depends on displacement, while speed depends on total distance traveled.

✔ The direction of velocity is always the same as the displacement of the object.

✔ The SI unit of velocity is the same as speed: m/s.

✔ When velocity is constant, acceleration is zero.

✔ An object moving with constant speed in a circular path has changing velocity.

Worksheet

1. Define velocity. Give an example.
2. Differentiate between speed and velocity.
3. A train moves with a speed of 60 km/hr towards the East. What is its velocity?
4. A boy moves 30 m North and then 40 m South in 10 seconds. Find his average velocity.
5. Explain why velocity is considered a vector quantity.

Test Paper (Total Marks: 20)

Section A: Conceptual Questions (10 Marks)

1. Define velocity and explain its SI unit. (2 Marks)
2. What is the difference between speed and velocity? (3 Marks)
3. Can a body have zero velocity and still be moving? Justify. (2 Marks)
4. A car moves 500 m towards North and then 500 m towards South in 50 sec. Calculate its velocity. (3 Marks)

Section B: Numericals (10 Marks)

1. A body covers 100 m in 20 sec in a given direction. Calculate its velocity. (2 Marks)
2. A cyclist moves 150 m due East in 15 seconds and then 50 m due West in 5 seconds. Find his average velocity. (3 Marks)
3. A train travels with a velocity of 72 km/hr. How much distance will it cover in 30 minutes? (5 Marks)

Quick Revision Points

✔ Velocity = Displacement / Time

✔ SI unit = m/s

✔ Scalar vs Vector : Speed is scalar, Velocity is vector.

✔ Uniform velocity : Equal distances in equal intervals.

✔ Non-uniform velocity : Speed or direction changes.

✔ Average velocity = Total displacement / Total time.

✔ Velocity can be zero if displacement is zero.

✔ Speed and velocity are equal in magnitude if motion is in a straight line without change in direction.

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