Speed and velocity both indicate how fast a body is traveling, but there is an important difference between these quantities. The average speed, v, of a body is given by its rate of change of distance, whereas the average velocity, v, of a body is its rate of change of displacement. The SI unit for both quantities is meters per second, m/s, but speed is a scalar quantity and velocity is a vector quantity.
If a car travels 200 meters in 10 seconds, we say its average speed is 20 meters per second, the average speed being the distance traveled divided by the time required to cover the distance:
Average speed = distance / elapsed time……………..(1)
Equation (1) indicates that the unit for average speed is the unit for distance divided by the unit for time, or meters per second (m/s) in SI units.
Speed is a useful idea because it indicates how fast an object is moving. However, speed does not reveal anything about the direction of the motion. To describe how fast an object moves and the direction of its motion, we need the vector concept of velocity.
To define the velocity of an object, we will use two concepts that we have already encountered, displacement and time.
Suppose in the above diagram, the initial position of the car is x0 when the time is t0. After some time it arrives at the final position x at time t. The difference between these times is the time required for the car to travel between the two positions. We denote this difference by the shorthand notation ∆t (delta t).
∆t = t – t0 = elapsed time
and as shown in the diagram above, displacement ∆x = x – x0
So the average velocity = displacement/elapsed time
= ∆x/∆t = (x – x0)/(t – t0) ……………(2)
Apart from this, as average velocity has a direction mentioned along with its magnitude, in this case, it may be written as along the positive x-axis.
Also Read: (suggested reading)
Difference between Instantaneous Speed and Instantaneous Velocity
Instantaneous Velocity – definition & equation with solved problem
Average velocity – definition, formula
Instantaneous Acceleration – definition & formula with solved problem
Average Acceleration and its formula & solved numerical problems