Concept of derivative of the function, Physics

Assignment Help:

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.


Related Discussions:- Concept of derivative of the function

Waves, some details about wave

some details about wave

Illustrate lenzs law, State and illustrate Lenz's law with examples Deri...

State and illustrate Lenz's law with examples Derive a mathematical expression for a force between two parallel conductors carrying a current.

Construction and working of nicol prism, Briefly explain with principle, th...

Briefly explain with principle, the construction and working of Nicol prism. Why the angle of incidence on Nicol prism would be around 14 o .

Explain the term capacitance of a capacitor, (a)   Explain the term 'capaci...

(a)   Explain the term 'capacitance' of a capacitor. Derive an expression for the total Capacitance of 'n' capacitors arranged in series. (b)   Explain the term 'capacitance' of

Electromagnetic radiations, Electromagnetic radiations: What are the c...

Electromagnetic radiations: What are the common features among all the Electromagnetic radiations? Ans: 1. They all can be described in terms of oscillating electric and ma

Reverse characteristic of a zener diode, Reverse Characteristic of a Zener ...

Reverse Characteristic of a Zener diode Reset voltage to  zero.  Connect  zener diode as shown in fig. and reverse characteristics are demonstrated in fig. Raise voltag

Determine average value of poynting vector, Show that average value of Poyn...

Show that average value of Poynting vector for a plane e-m wave is  1/2 √μ/e XH 2 .

Lab, Imagine a small observer is positioned in front of the cork in your pi...

Imagine a small observer is positioned in front of the cork in your picture above. As the cork approaches, the observer measures the wavelength of the waves passing by. How does th

Particle detectors, what is the principle of particle detectors ?

what is the principle of particle detectors ?

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd