Question

Define average velocity and instantaneous velocity. When are they the same?

Answer 1

Hint: Average velocity is defined as the ratio of total displacement done by the body to the time taken by the body. While, instantaneous velocity is defined as the velocity of a body at a specific point of time i.e. displacement of a body at a specific point of time. At only one condition, average velocity and instantaneous velocity will become the same when the velocity is constant.

Complete solution:
Average velocity is more of an imaginary velocity. For a particular displacement and the total time actually taken to get from point A to point B if the particle would have travelled at one velocity throughout (i.e. if the motion would have been uniform) then the value of that velocity is equal to the average velocity.
Thus, average velocity is given by,
$Average\ velocity= \dfrac {Total\ displacement}{Total\ time\ interval}$
$\Rightarrow {V}_{avg}= \dfrac {{X}_{final}-{X}_{initial}}{{T}_{final}-{T}_{initial}}$
On the other hand, instantaneous velocity can be defined as the velocity at a particular instant of time. Thus, if we draw a velocity time graph, at every instant of time then the value of velocity would be the instantaneous velocity.
Thus, instantaneous velocity is given by,
${V}_{instant}= \dfrac {dX}{dT}$
Instantaneous velocity and average velocity will be the same when the velocity of body is constant or the acceleration is zero on the grounds that in condition all the instantaneous velocities will be equivalent to one another and furthermore equivalent to average velocity.

Note:
Students must remember that the average velocity of a particle in a closed loop is always zero when the object moves from the same point. Instantaneous velocity gives the truer idea of a particle’s motion. Velocity, average velocity and instantaneous velocity have the same S.I unit i.e. ${m}/{s}$. The value of average velocity or instantaneous velocity can be positive, negative or zero.