Concept of derivative of the function, Physics

KINEMATICS II

1. The concept of the derivative of the function is exceptionally important. The derivative shows that how fast the function changes when its argument is changed. (Remember that for f ( x) we say that is a function that depends upon the argument x. You should think of as a machine which gives you the value when you input x.)

 

2.  Functions do not always have to be written as f ( x). us where a body is at different times t.

 

3. The derivative of x(t ) at time t can be defined as:

1433_derivative of x.png

2417_derivative of x1.png

4. Now let's see how to calculate the derivative of a simple function such as  x(t ) = t 2 . We should first calculate the difference in x at two slightly different values say, t and t + Δt, while that recall we choose Δt to be extremely small:

606_derivative of x2.png

5. In exactly the same manner you can show that if x(t ) = t n  then:

1879_derivative of x3.png

This is an exceptionally useful result.

Posted Date: 7/26/2012 1:58:14 AM | Location : United States







Related Discussions:- Concept of derivative of the function, Assignment Help, Ask Question on Concept of derivative of the function, Get Answer, Expert's Help, Concept of derivative of the function Discussions

Write discussion on Concept of derivative of the function
Your posts are moderated
Related Questions
What is the resistance of a coil of aluminium wire The resistance of a coil of aluminium wire at 18 ? C is 200?. The temperature of the wire is increased and the resistance

A vernier callipers gives with an auxiliary (or vernier) scale in addition to the major measurement scale. The vernier scale may be slide with the main scale. The vernier scale is

Action and reaction with a roller skate Place a roller skate on a smooth floor. Step on the roller skate with one foot and take a step forward with the other. Observe that the

N-Type Substances: When a small quantity of Arsenic or Phosphorous (group VA elements) is added to silicon or Germanium, it becomes good conductor of negative charges, such a s

A lead bullet moves horizontally with a velocity of 130 ms-1 and embedded into a cement wall after collision. If the specific heat capacity of lead = 130 JKg-1°C-1 and all heat pro

A ball leaves a girl's hand with an upward velocity of 6 meters per second.  What is the maximum height of the ball above the girl's hand? Ans: A ball leaves a girl's hand w

Monochromatic light (single wavelength) falls on two narrow slits S1 and S2 which are very close together acts as two coherent sources, when waves coming from two coherent sources

#question.what isthe range of thermoelectric thermometer?.

Measurement of length: If the Zeroth division of the head scale does not coincide with the index line the Screw gauge has Zero error. If the Zeroth division of the head Sca

Particles of the medium implement simple harmonic motion about their mean position in a direction perpendicular to the direction of propagation of wave motion. (i) It goes in th