How to derive mathematical formula o newton's 2nd law of motion?
Answers
Mathematical Formulation of Second Law of Motion
Let us consider an object of mass m, moving along a straight line with an initial velocity u. Let us say, after a certain time t, with a constant acceleration, the final velocity becomes v.
Here we see that, the initial momentum
Law Of Motion
The final momentum
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The change in momentum can be written as
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As we know, the rate of change of momentum with respect to time is proportional to the applied force.
The applied force
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Or,
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as acceleration (a) = rate of change of velocity with respect to time.
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where k = constant of proportionality.
The SI units of mass and acceleration are kg and m s-2 respectively.
So,
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The second law of motion gives us a method to measure the force acting on an object as a product of mass of the object and the acceleration of the object which is the change in velocity with respect to time.
Newton's Second Law
Newton's Second Law
The Big Misconception
Finding Acceleration
Finding Individual Forces
Free Fall and Air Resistance
Double Trouble
Newton's first law of motion predicts the behavior of objects for which all existing forces are balanced. The first law - sometimes referred to as the law of inertia - states that if the forces acting upon an object are balanced, then the acceleration of that object will be 0 m/s/s. Objects at equilibrium (the condition in which all forces balance) will not accelerate. According to Newton, an object will only accelerate if there is a net or unbalanced force acting upon it. The presence of an unbalanced force will accelerate an object - changing its speed, its direction, or both its speed and direction.