• Speed

The distance covered by an object in unit time is called distance or It can be defined as the time rate of change of distance of an object. Therefore,

Speed = Distance covered / Total time taken

⇒ v = st

Where, v = speed, s = distance, t = total time.

Note:

1. Speed is a scalar quantity.
2. Speed is either positive or zero but never negative.
3. Speed of a running car is measured by ‘speedometer’.
4. Speed is measured in cm/s in cgs system of units, m/s in SI system of units and km/h in practical life when distance and time involved are large.

If a body is executing uniform motion, then there will be a constant speed or uniform motion. If a body is travelling with non-uniform motion, then the speed will not remain uniform but have different values throughout the motion of such body. For non-uniform motion, average speed will describe one single value of speed throughout the motion of the body.

For non-uniform motion, we define two definitions:

Average speed: The average distance covered in unit time by a moving object is called average speed. Average speed is define as the ratio of total distance covered to total time taken. Therefore,

Average speed = Total distance covered / Total time taken

⇒ v = st

Where, v = Average Speed, s = Total distance covered, t = total time taken.

Let a car covers first 25 km in 1 h, next  35 km in ½ h and last 30 km in 1 h, then the average speed is = (25 + 35 + 30) / (1 + ½ +1) = 36 km/h.

Instantaneous Speed: When a body is moving with variable speed, the speed of the body at any instant is called instantaneous speed.

Velocity

It is defined as the time rate of change of displacement of a body or as the distance travelled by a body in unit time in a given direction. Therefore,

Velocity = Displacement / Time taken

⇒ v = st

Note:

1. Velocity is a vector quantity.
2. Velocity can either positive, negative or zero.
3. Direction of velocity is the same as the direction of displacement of the body.
4. Velocity can be changed in two ways:

i) by changing the speed of the body or

ii) by keeping the speed constant but by changing the direction.

5. Velocity is measured in cm/s in cgs system of units, m/s in SI system of units and km/h in practical life when distance and time involved are large.

Uniform Velocity: A body is said to be moving with uniform velocity (constant velocity), if it travels in a specified direction in a straight line and moves over equal distances in equal intervals time, no matter how small these time intervals may be.

Non-Uniform Velocity: A body is said to be moving with non-uniform velocity (variable velocity), if its speed or its direction or both change(s) with time.

For example, if a vehicle is moving on a circular path with uniform speed, then its velocity is said to be non-uniform, because on a circular path the direction of moving body changes along with direction of curve.  If a vehicle moving with uniform speed on a jig-jag path, the velocity of the vehicle will be non-uniform because direction of vehicle is changed with the change of direction of path.

For non-uniform velocity, we define two definitions:

Average Velocity: The arithmetic mean of velocity of an object moving along a straight line is called the average velocity. The displacement of a moving object in unit time is also called the average velocity.

Here, average velocity will be calculated in the same way as done in average speed. Therefore,

Average velocity = Displacement / Time taken

For uniformly changing velocity, the average velocity can be calculated as follows :

Average velocity = (Initial velocity + Final velocity) / 2

vav = (u + v) / 2

where, u = initial velocity, v = fnal velocity

Instantaneous Velocity: When a body is moving with variable velocity, the velocity of the body at any instant is called instantaneous velocity. Comparison between Speed & Velocity 