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**The Course Designed based on the pattern of NCERT.Useful and advanced content are added as per Edusaint's Learning framework to enable the student to prepare for IIT foundation and other Relevant exams.**

**Velocity is the rate of change in an object’s position.**- Velocity has a magnitude (speed) and a direction.
- Velocity is a vector quantity.
- Velocity is represented by the formula:

**Velocity = the change in distance/change in time**

**Velocity = Δx/Δt**

**Velocity has the same unit of measure as speed.****The standard unit of measure is meters per second or m/s.**

**Uniform Velocity (or Constant Velocity)**

- If an object travels in a specified direction in a straight line and moves the same distance every second,
- we say that its velocity is uniform. Thus, A body has a uniform velocity if it travels in a specified direction in a straight line and moves over equal distances in equal intervals of time, no matter how small these time intervals may be.

**What is the difference between speed and velocity?**

**Speed is the magnitude of velocity. Velocity is the speed of an object plus its direction. Speed is called a scalar quantity and velocity is a vector quantity.**

**Speed of Light**

**The fastest possible speed in the universe is the speed of light. The speed of light is 299,792,458 meters per second.****In physics this number is represented by the letter “c.”**

**Interesting Facts about Speed and Velocity**

- The first scientist to measure speed as distance over time was Galileo.
- A speedometer is a great example of instantaneous speed.
- The speed of light can also be written as 186,282 miles per second.
- The speed of sound in dry air is 343.2 meters per second.
- The escape velocity of Earth is the speed needed to escape from Earth’s gravitational pull. It is 25,000 miles per hour.

**Sample problem**

**Problem.**

A man walks 7 km in 2 hours and 2 km in 1 hour in the same direction.

a) What is the man’s average speed for the whole journey?

b) What is the man’s average velocity for the whole journey?

average speed = | distance
time |
= | 7 km + 2 km
2 hours + 1hour |
= | 9 km
3 hours |
= 3 km/h |

b)

average velocity= | displacement
time |
= | 7 km + 2 km
2 hours + 1hour |
= | 9 km
3 hours |
= 3 km/h |

- During uniform motion of an object along a straight line, the velocity remains constant with time. In this case, the change in velocity of the object for any time interval is zero.
- However, in non-uniform motion, velocity varies with time. It has different values at different instants and at different points of the path.
- Thus, the change in velocity of the object during any time interval is not zero.
- When the velocity of a body is increasing, the body is said to be accelerating. Suppose a car starts off from rest (initial velocity is zero) and its velocity increases at a steady rate so that after 5 seconds its velocity is 10 metres per second. Now, in 5 seconds the velocity has increased by 10 – 0 = 10 metres per second and in 1 second the velocity increases by 10/2 =5 metres per second.
- In other words, the rate at which the velocity increases is 2 metres per second every second. The car is said to have an acceleration of 2 metres per second per second.
- This gives us the following definition of acceleration: Acceleration of a body is defined as the rate of change of its velocity with time. That is,

Acceleration = Change in velocity/Time taken for change

- Now, the change in velocity is the difference between the final velocity and the initial velocity. That is,
- Change in velocity = Final velocity – Initial velocity

**Misconception**

- A common misconception about velocity and acceleration has to do with their directions.
- Since velocity has both magnitude and direction, a change in either magnitude (speed) and/or direction will result in a change in velocity, therefore an acceleration. We can accelerate objects either by speeding them up or down (change magnitude) and/or by changing their directions of travel.
- For motion in one-dimension, when the velocity and acceleration of an object are in the same direction (they have the same directional signs), the velocity increases and the object speeds up (acceleration). When the velocity and acceleration are in the opposite direction, the velocity decreases and the object slows down (deceleration).

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