Integration by Substitution
If u is a function of x, we can use the following formula to evaluate an integral. f dx = (f/(du/dx)) du Using the Formula Use of the formula is equivalent to the following procedure: 1. Write u as a function of x..
Mirror Formula
In a spherical mirror, the distance of the object from its pole is called the object distance (u). the distance of the image from the pole of the mirror is called the image distance (v). You already know that the distance of the principal focus from the pole is called the focal length (f..
In a spherical mirror, the distance of the object from its pole is called the object distance (u). the distance of the image from the pole of the mirror is called the image distance (v). You already know that the distance of the principal focus from the pole is called the focal length (f..Second Equation of Motion
From equations (1) and (2) The first equation of motion is v = u + at. Substituting the value of v in equation (3), we get ..
From equations (1) and (2) The first equation of motion is v = u + at. Substituting the value of v in equation (3), we get ..Third Equation of Motion
Substituting the value of t in equation (1) we get, 2aS = (v + u) (v - u) (v + u)(v - u) = 2aS [using the identity a 2 - b 2 = (a+b) (a-b)] v 2 - u 2 = 2aS III Equation of Moti..
Substituting the value of t in equation (1) we get, 2aS = (v + u) (v - u) (v + u)(v - u) = 2aS [using the identity a 2 - b 2 = (a+b) (a-b)] v 2 - u 2 = 2aS III Equation of Moti..Factorisation using the identity
Let x + y = u Substitute x + y for u..
Let x + y = u Substitute x + y for u..Mirror Formula
from the above two equations we have Since all distances are measured from P CB = PB - PC CB l = PC - PB l Therefore, Using the sign convention, PB = - u (object distance) PC = -R PB = -v (Image distance) On substitution, +uR - uv = uv - vR uR + vR = 2uv Divi..
from the above two equations we have Since all distances are measured from P CB = PB - PC CB l = PC - PB l Therefore, Using the sign convention, PB = - u (object distance) PC = -R PB = -v (Image distance) On substitution, +uR - uv = uv - vR uR + vR = 2uv Divi..Third equation of motion.
Substituting the value of t in eq. (1) we get, (v + u)(v - u) = 2as [using the identity a 2 - b 2 = (a+b) (a-b)] v 2 - u 2 = 2as III Equation of Moti..
Substituting the value of t in eq. (1) we get, (v + u)(v - u) = 2as [using the identity a 2 - b 2 = (a+b) (a-b)] v 2 - u 2 = 2as III Equation of Moti..Expression for Kinetic Energy of a Moving Body
Consider a body of mass 'm' which is initially at rest. When a force 'F' is applied on the body, let it start moving with a velocity 'v' and cover a distance 'S'. The force produces acceleration 'a' in the body. The force 'F' does work when it moves the body through a distance 'S' and this work d..
Consider a body of mass 'm' which is initially at rest. When a force 'F' is applied on the body, let it start moving with a velocity 'v' and cover a distance 'S'. The force produces acceleration 'a' in the body. The force 'F' does work when it moves the body through a distance 'S' and this work d..See what our Users say :
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