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GDB Dated: Aug 04, 14

Dear Student,
The following is the topic for GDB


 

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

 

(Be precise to this topic only)

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

Dear Student,

The following is the topic for GDB

“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”

(Be precise to this topic only)

Opening Date: Aug 07(Thursday), 2014 at 12:01 AM

Closing Date: Aug 08(Friday), 2014 at 11:59 PM

Instructions:.

(1) Post your comments only on the concern Graded MDB forum and not on regular MDB forum.

(2) Write your comments in the plain text and avoid math type symbols and figures/graphs/images as these will not appear on the board.

(3) Zero marks will be given to irrelevant comments or to those which are copied from website or any other source.

(5) Do not enter your comments more than once.

(6) Due date will not be extended.

(7) No description will be accepted through e-mail.

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.
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.

kia yeh pura solution ha? agr ni ha to pleas pura solution snd kr dain

MTH101 

Instantaneous velocity
In order to under to understand the concept of the instantaneous velocity, Consider a body moving along a path ABC in plane. At any time t, let the body at the point A. Its position is given by position vector r1.After a very short time interval following of the instant t, the body reach the point B which is described the by the position vector r2.The displacement of the body during is short time interval given by 
Deltad=r1-r2 
The instantaneous velocity is define as the limiting value of delta d/dt as the time interval following the time t, approaches zero,
Vins delta t >0 delta d / delta t

The instantaneous velocity does not change the body is said to be moving with uniform velocity.
Average velocity 
Time rate of change displacement is known as the velocity. Its direction is along the direction of displacement of the body in the time of t, is defining as Vav =d/t
Average velocity does not tell us about the motion between A and B. For example if a squash ball comes back its starting point after bouncing off the wall several times, its total displacement is zero and also its average velocity. In such cases the motion is describe by the instantaneous velocity. 
When we accelerate or decelerate the instantaneous and average velocity same. Infect at the some points they have to be equal.

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