Average Velocity and Instantaneous Velocity

You know that, speed is related to distance and is a scalar quantity. Similarly, velocity is a vector quantity which is related to displacement of the particle.

You can easily find the velocity of a particle if you know the displacement. From previous section you have studied how to calculate displacement in a 3 dimensional space.

Average velocity of a particle in a time interval t1 to t2 is defined as its displacement divided by the time interval.

Please note in mind that, we need just initial and final position of the particle to calculate average velocity.ie, the position in between t1 and t2 need not to bother.

 Instantaneous velocity is the velocity at a given location in a time.
For a very small interval of time the displacement ∆r, will be along the line of motion of the particle. In this small interval of time the distance and displacement will be equal. Which means, magnitude of instantaneous speed and instantaneous velocity are same.

At the school time, I had a doubt that when will be the velocities become zero and negative? Do you have the same? No need to worry. Here I would like to explain the concept, with figure 3 shown below.

In the figure 3, at initial stage displacement is increasing. This means, slope of the curve is positive. ie, velocity is positive at this stage. But at peak, the change of displacement with respect to time is zero. Velocity is zero at that position. At final stage of journey, the displacement is decreasing with respect to time which leads to a negative velocity.

Figure 3