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How to Calculate the force given potential energy
For one dimensional motion, the force can be found from Potential energy using following formula
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Common mistake doing average speed calculation
Two most common errors you should avoid when you see an average speed question.
Mistake #1
The most common mistakes in average speed problems occurs when the question asks you to calculate the average speed of a object moving at two different speeds for different parts of the journey. Students are generally tempted to calculate the arithmetic mean (average) of the two speeds, and select a corresponding answer. This averaging approach is wrong.
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Integration of sin square x and sin 2x
Integration of sin square x can be calculated using trigonometric identities .Here is the formula for it $$ \int \sin^2(x) \, dx = \frac{1}{2} x – \frac{1}{4} \sin(2x) + C $$ Integration of sin 2x can be calculated using integration by substitutions .Here is the formula for it $$ \int \sin(2x) \, dx= \frac {-cos
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integration of cot square x
The integration of cot square x $\cot ^2 x$, can be found using trigonometry identities and fundamental integral formulas . The integral of $\cot^2 x$ with respect to (x) is: \[\int \cot^2 x \, dx =-\cot x -x + C\] Here, (C) represents the constant of integration, which is added because the process of integration
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integration of tan square x
The integration of tan square x $\tan ^2 x$, can be found using trigonometry identities and fundamental integral formulas . The integral of $\tan ^2 x$ with respect to (x) is: \[\int \tan^2 x \, dx =\tan x -x + C\] Here, (C) represents the constant of integration, which is added because the process of
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Acceleration formula Explained with Examples
Acceleration Formula Acceleration is the rate of change of velocity with time. It is a measure of the change in the velocity of an object per unit time and mathematically acceleration formula is given as For describing average acceleration, we first consider the motion of an object along a straight line.Suppose at time t1 object is at
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How to apply law of conservation of energy in mechanics
We often comes across the problems in mechanics where we need to apply the law of conservation of energy where gravitational potential energy or gravity is involved . For solving such problems you can consider the following problem solving strategy,
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How to solve Simple Harmonic Motion(SHM) problems effectively for JEE Main/Advanced
What is Periodic Motion : In Physics, a motion that is regular and repeating is called Periodic Motion. The time to complete one full motion is called the Time period of the Periodic Motion
What is SHM: A Simple Harmonic Motion is a special case of Periodic motion where a physical quatity varies sinusoidally.In this Periodic motion the restoring force is directly proportional to the displacement. The object oscillates between two position and Motion is sinusoidally in nature.
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