Question

Why is $\mathrm{displacement}=\mathrm{average}\mathrm{velocity}\mathrm{x}\mathrm{time}$, only when velocity is constant?

Answer 1

Velocity:

1. Velocity can be defined as the rate of change of the object’s position with respect to a frame of reference and time.
2. The SI unit of velocity is meter per second $\left({\mathrm{ms}}^{-1}\right)$.

Explanation:

1. Average velocity is the total displacement by total time and is given by $v=\frac{∆x}{∆t}$, where $∆x$ is the total displacement of the body and $∆t$ is the time.
2. Instantaneous velocity is the velocity of a body at any given time.
3. When a particle is moving with constant velocity then its magnitude and direction both are not changing means the particle must travel in a straight line. Also when the particle is moving in a straight line with no acceleration then the distance covered and displacement will be the same in the same interval of time.
4. When the acceleration is zero or the velocity is constant, instantaneous velocity equals average velocity since all of the instantaneous velocities are equal to each other and to the average velocity.
5. The velocity at any instance is obtained from the average velocity by shrinking the time interval $∆t$ close to zero.

$$\begin{gathered} v=\underset{∆t\to 0}{\lim }\frac{∆x}{∆t} \\ v=\frac{d\mathrm{x}}{d\mathrm{t}} \end{gathered}$$

5. The above graph is a graph of displacement versus time for a body moving with constant velocity.

6. Mathematically, displacement can be represented as:

$\mathrm{Displacement}\left(\mathrm{d}\right)=\mathrm{Velocity}\left(\mathrm{v}\right)\times \mathrm{Time}\left(\mathrm{t}\right)$

When the particle is moving in a straight line with no acceleration then the distance covered and displacement will be the same in the same interval of time.

Thus, $\mathrm{displacement}=\mathrm{average}\mathrm{velocity}\mathrm{x}\mathrm{time}$, when velocity is constant.