Question

when is the average velocity of an object equal to the instantaneous velocity?
always
never
only when the velocity is constant
only when the velocity is increasing at a constant rate

Explanation:

• Average velocity is calculated as the total displacement divided by the total time taken ($v_{avg}=\frac{\Delta x}{\Delta t}$).
• Instantaneous velocity is the velocity of an object at a particular instant in time.
• When the velocity is constant, the value of velocity does not change over time. So, for any time interval $\Delta t$, the displacement $\Delta x = v\times\Delta t$ (where $v$ is the constant velocity). Then $v_{avg}=\frac{v\times\Delta t}{\Delta t}=v$, which is equal to the instantaneous velocity (since $v$ is constant at every instant).
• If the velocity is changing (either increasing, decreasing, or changing in direction in a non - uniform way), the average velocity over a time interval will not be equal to the instantaneous velocity at most instants within that interval. For example, in a non - uniform acceleration (where velocity is increasing at a non - constant rate) or even in a case of constant acceleration (where velocity is increasing at a constant rate, $v = u+at$), the average velocity over a time interval (for constant acceleration $v_{avg}=\frac{u + v}{2}$ where $u$ is the initial velocity and $v$ is the final velocity) is not equal to the instantaneous velocity at most points in the time interval (except in some special cases related to the mid - point of time or displacement which is more of a derived result for constant acceleration and not a general equality).

Answer:

only when the velocity is constant