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|GDB||Dated: Aug 04, 14|
“What's the difference between instantaneous and average velocity? How do you calculate both of them? Also discuss under what circumstances both velocities become same”
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Opening Date: Aug 07(Thursday), 2014 at 12:01 AM
Closing Date: Aug 08(Friday), 2014 at 11:59 PM
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MTH-101 GDB IDEA SOLUTION
Instantaneous velocity is the velocity of an object in motion at a specific point in time.
Instantaneous velocity is a measure of an object's velocity at any instant in time
The average velocity of an object over a given period of time is found by dividing the distance it has traveled by the time elapsed. Because velocity refers to the rate at which an object changes position, it is a vector quantity and direction matters..
Total distance in that direction, divided by total time
when both velocities become same:-
Average velocity is equal to the instantaneous velocity when acceleration is zero. In order for acceleration of an object to equal zero, there can be no change in speed or direction. For example, when a car is traveling down a straight road on flat land using cruise control.
Average velocity = the distance traveled divided by the amount of time it took to travel that distance.
Distance = average speed X time traveled, the most basic of all the kinematic relationships. In math talk, that's S = Vavg T using standard SUVAT notation.
So Vavg = S/T. So any time we have an interval called distance, S, and a commensurate time interval, T, Vavg is appropriate. It's similar for the acceleration as Aavg = (V - U)/T. So when there is a speed interval (V - U) and a T interval, we have average acceleration. U is the starting speed and V is the end speed.
Now here's the fun part.
If we make those S, T, and (V - U) intervals shrink until they're very tiny, we can write V = dS/dT or A = dV/dT where the d* means very tiny interval. And there is the so-called instantaneous speed V and acceleration A. And there's the horrible truth. In math there is no such thing as instantaneous. It's just an average over a very tiny interval.
There is, of course, a formal math way to define dS/dT and dV/dT, but unless you've taken differences and differential equations that would only confound things to bring it up. Just remember, if the interval is so very tiny as to be insignificant; then that's instantaneous.
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