Question

Explain the terms the average velocity and instantaneous velocity. When are they equal?

Answer 1

Step 1: Average velocity

1. It is the ratio of total displacement to total time. $v_{avg}=\frac{\mathrm{Total}\mathrm{displacement}}{\mathrm{Total}\mathrm{time}}=\frac{∆x}{∆t}=\frac{x_2-x_1}{t_2-t_1}$
2. Average velocity is a vector quantity.
3. SI unit is meters per second.

Step 2: Instantaneous velocity

1. The velocity at a specific instance of time is called instantaneous velocity.
2. Instantaneous velocity is a vector quantity.
3. SI unit is meters per second.

Step 3: Conditions for average velocity and instantaneous velocity to be equal are:

1. 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.
2. The velocity at any instance is obtained from the average velocity by shrinking the time interval $∆t$ close to zero.

$v=\underset{∆t\to 0}{lim}\frac{∆x}{∆t}=\frac{dx}{dt}$