Question

Answer the following question.

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

Answer 1

Average velocity:

1. Average velocity `(vec"v"_"av")` of an object is the displacement `(Delta vec"X")` of the object during the time interval (Δt) over which average velocity is being calculated, divided by that time interval.
2. Average velocity =`("Displacement"/"Time interval")`
   `vec"v"_"av" = (vec"x"_2 - vec"x"_1)/("t"_2 - "t"_1) = (Deltavec"x")/(Delta "t")`
3. Average velocity is a vector quantity.
4. Its SI unit is m/s and dimensions are [M⁰L¹T^-1]
5. For example, if the positions of an object are x = +4 m and x = +6 m at times t = 0 and t = 1 minute respectively, the magnitude of its average velocity during that time is `"v"_"av"` = (6 - 4)/(1 - 0) = 2 m per minute and its direction will be along the positive X-axis.
   ∴ `vec"v"_"av"` = 2 i m/min
   where, i = unit vector along X-axis.

Instantaneous velocity:

1. The instantaneous velocity `(vec"v")` is the limiting value of the average velocity of the object over a small time interval (Δt) around t when the value of time interval goes to zero.
2. It is the velocity of an object at a given instant of time.
3. `vec"v" = lim_(Delta"t"->0) (Delta vec"x")/(Delta "t") = ("d"vec"x")/"dt"`
   where `("d"vec"x")/"dt"` = derivative of `vec"x"` with respect to t.

In the case of uniform rectilinear motion, i.e., when an object is moving with constant velocity along a straight line, the average and instantaneous velocity remain the same.