Question

Why is $\text{displacement = Avg. velocity}\time \text{time}$ only when velocity is constant ?

Answer 1

Hint:Displacement is defined as a change in an object's position. It is a vector quantity with a magnitude and a direction. It is represented by an arrow pointing from the starting point to the ending point. For instance, if an object moves from A to B, the object's position changes.

Complete step by step answer:
Displacement is defined as a change in an object's position. The following equation can be used to define it mathematically:
\[Displacement={{\Delta }_{x}}={{x}_{f}}-{{x}_{0}}\]
Velocity is defined as the speed of a body in a specific direction. Velocity is defined as the rate of change in displacement concerning time. Velocity is a vector quantity that has a magnitude as well as a direction. Velocity is a measure of how long it takes an object to travel in a straight line to its destination.

Your understanding of velocity is most likely similar to its scientific definition. You are aware that a large displacement in a short period indicates a high velocity, and that velocity is measured in units of distance divided by time, such as miles per hour or kilometers per hour.
The average velocity is defined as the position change divided by the time of travel.
\[{{\upsilon }_{avg}}=\dfrac{{{\Delta }_{x}}}{{{\Delta }_{t}}}=\dfrac{{{x}_{f}}-{{x}_{0}}}{{{t}_{f}}-{{t}_{0}}}\]
Here, \[{{\upsilon }_{avg}}\]=Average velocity, \[{{\Delta }_{x}}\]= The change in position, or displacement, \[{{x}_{f}}\] and \[{{x}_{0}}\]=final and beginning positions at times ${{t}_{f}}$ and ${{t}_{0}}$, respectively.

If the starting time ${{t}_{0}}$ is taken to be zero, then the average velocity is written as below:
\[{{\upsilon }_{avg}}=\dfrac{{{\Delta }_{x}}}{t}\]
If, \[t\] is shorthand for \[{{\Delta }_{t}}\]
Thus, when velocity is constant, displacement = Avg. velocity x time is given as,
\[{{\upsilon }_{avg}}=\dfrac{{{\Delta }_{x}}}{t} \\
\Rightarrow {{\upsilon }_{avg}}\times t={{\Delta }_{x}} \\
\therefore {{\Delta }_{x}}={{\upsilon }_{avg}}\times t \]

Note:However, the average velocity of an object tells us nothing about what happens to it between the starting and ending points. For example, average velocity cannot tell us whether an airplane passenger stops briefly or backs up before proceeding to the back of the plane. To obtain more information, we must consider smaller segments of the journey over shorter time intervals.