ultimate physics tutor


2. Show that the function $\phi$: R→R defined by $\phi$(x) = $e^{-x}$ + 2 is the solution of the differential equation y' + y = 2, y(0) = 3.
Solution: $\phi$(x) = e -x + 2 => $\phi$'(x) = -e -x If we replace y by $\phi$(x), we have y'+ y = $\phi$'(x) + $\phi$(x) = -e -x + e -x + 2 = 2 $\phi$ (x) satisfies the equation y' + y = 2 Moreover, $\phi..
Physics and technology
The technological development of any society is very closely related with the application of physics and other branches of science. The study of heat and thermodynamics is one of the main initiators of the industrial revolution. Today we see the applications of physics in eve..
INTRODUCTION TO PHYSICS
What is Physics? The word "Physics" comes from a Greek word "fusis" and its meaning is "nature". Physics as a subject can be regarded as the study of nature and natural phenomena...
NUCLEAR PHYSICS
The discovery of radio - activity marked the beginning of the development of nuclear physics. Rutherford's discovery of nucleus and the artificial radio-activity have shown that nucleus has got its own structure. The structure and properties of the nucleus was further established b..
Physical Equilibrium
Equilibrium is also attained in physical processes such as vaporization and condensation. The conversion of a liquid into vapour is known as vaporization, while the opposite process, i.e., the conversion of a vapour into liquid is called condensation. The molecules of a liquid that..
PHYSICAL PROPERTIES
1. Physical state: Dimethyl ether and ethyl methyl ether are gases at room temperatures. Other lower members are colourless liquids, which are highly volatile. 2. Boiling points: Ethers have much lower boiling points compared to isomeric alcohols as they are not associated with..
Physical properties
(1) Taste : Acids have a sour taste. Mineral acids like H 2 S0 4 and HN0 3 are highly corrosive in nature. Therefore, they should not be tasted. (2) Physical state : Some acids are solids and some are liquids at room temperature. For example : ..
MODERN PHYSICS
X-rays were discovered by Rontgen in 1895. Becquerel, in 1896, performed some experiments. He observed that salts of uranium affect a photographic plate covered with black paper after several hours of exposure. Becquerel further discovered that such radiations are the property of uranium salt. As..
PHYSICAL OPTICS
Phenomena of light such as reflection, refraction, formation of images by mirrors and lenses are successfully explained by the assumption that light travels in straight lines. In all these phenomena light interacts with objects whose size is much larger than the wavelength of light (of the o..