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Preeti Dabral 7 years, 11 months ago
Instantaneous velocity is defined as the rate of change of position for a time interval which is very small (almost 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 and time is non zero and is called the instantaneous velocity.
Instantaneous Velocity
If the displacement of the particle varies with respect to time and is given as (6t2 + 2t + 4) m, the instantaneous velocity can be found out at any given time by:
s = (6t2 + 2t + 4)
Velocity (v) = dsdt
= d(6t2+2t+4)dt
= 12t + 2
So if we have to find out the instantaneous velocity at t = 5sec, then we will put the value of t in the obtained expression of velocity.
Instantaneous velocity at t = 5 sec = (12×5 + 2) = 62 m/s
Let us calculate the average velocity now for 5 seconds now.
Displacement = (6×52 + 2×5 + 4) = 164 m
Average velocity = 1645 = 32.8 m/s
Instantaneous Speed:
We know that the average speed is for a given time interval is total distance travelled divided by the total time taken. As this time interval approaches zero, the distance travelled also approaches zero. But the limit of the ratio of distance and time is non zero and is called the instantaneous speed.
To understand it in simple words we can also say that instantaneous speed at any given time is the magnitude of instantaneous velocity at that time.
If distance as a function of time is known to us, we can find out the instantaneous speed at any time. Let’s understand this by the means of an example.
Distance (s) = 5t3 m
Speed (v) = dsdt
= d(5t3)dt
= 15t2
We can now easily find the instantaneous speed at any given time by putting the value of t in this obtained expression.
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Amar Kumar 8 years, 3 months ago
Law of conservation of energy states that the total energy of an isolated system in a given frame of reference remains constant—it is said to be conserved over time. Energy can neither be created nor destroyed; rather, it transforms from one form to another.
For instance, chemical energy can be converted to kinetic energy in the explosion of a stick of dynamite. In technical terms, conservation of energy can be rigorously proven by the Noether theorem to be a direct consequence of continuous time translation symmetry.
Posted by Tarachand Verma 8 years, 3 months ago
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Amar Kumar 8 years, 3 months ago
Elasticity is the ability of a body to resist a distorting influence or deforming force and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate forces are applied on them. If the material is elastic, the object will return to its initial shape and size when these forces are removed.
The physical reasons for elastic behavior can be quite different for different materials. In metals, the atomic lattice changes size and shape when forces are applied (energy is added to the system). When forces are removed, the lattice goes back to the original lower energy state. For rubbers and other polymers, elasticity is caused by the stretching of polymer chains when forces are applied.
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