Answer to Question #148812 in Atomic and Nuclear Physics for daud

Question

a) What is the difference between Instantaneous Velocity and Average Velocity? Give detail with suitable examples.

Answer 1

Instantaneous velocity is velocity at a specific point in time and space. Mathematically, it is a derivative: the slope of the “position vs time” curve at one particular point.

$\displaystyle v_{inst} = \frac{dx}{dt} |_{t=t_0}$

Average velocity is velocity over some defined interval:

$\displaystyle v_{avr} = \frac{x_{final} - x_{initial}}{t_{final} - t_{initial}}$

For example, in case of a car that rides at first uphill and then downhill, the instantaneous velocity uphill may be 20mph, dowhill 50mph. If at the end of the way car crashes into some tree, the instantaneous velocity at this point will be zero. If the whole way was 10 miles and it was passed in 15 minutes, the average velocity over the whole way will be 40 mph. This tells us nothing about the specific features of the path (going slower uphill, faster downhill, crash at the end), but this quantity is useful e.g. for estimation our time for future trips.