Name: Inertial Frames of Reference
Uploaded: 2019-07-19
Duration: 7 min 10 s
Description: Imagine if you are on a bus or a train, can you say you are in an inertial frame of reference? If yes, how can you predict it? Let us explore more in this vi...

Question

Define instantaneous velocity. Explain how we may get instantaneous velocity of a particle moving with a variable velocity if we know its displacement time graph.

Accepted Answer

The instantaneous velocity of an object is the limit of the average velocity as the elapsed time approaches zero.

We know that the average velocity for a given time interval is total displacement divided by total time. As this time interval approaches zero, the displacement also approaches zero. But the limit of the ratio of displacement to time is non-zero and is called instantaneous velocity.

The instantaneous velocity is the specific rate of change of position (or displacement) with respect to time at a single point, while average velocity is the average rate of change of position (or displacement) with respect to time over an interval.

The instantaneous velocity at a specific time point $t_{0}$ is the rate of change of the position function, which is the slope of the position function $x (t)$ at $t_{0}$ . Figure shows how the average velocity $v = \frac{∆ x}{∆ t}$ between two times approaches the instantaneous velocity at $t_{0}$ . The instantaneous velocity is shown at time $t_{0}$ , which happens to be at the maximum of the position function. The slope of the position graph is zero at this point, and thus the instantaneous velocity is zero. At other times, $t_{1}, t_{2}$ , and so on, the instantaneous velocity is not zero because the slope of the position graph would be positive or negative. If the position function had a minimum, the slope of the position graph would also be zero, giving an instantaneous velocity of zero there as well. Thus, the zeros of the velocity function give the minimum and maximum of the position function.

Define instantaneous velocity. Explain how we may get instantaneous velocity of a particle moving with a variable velocity if we know its displacement time graph.

Important Questions on Motion of a Particle

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