The second law of motion states that any acceleration in an object or body as a result of a force acting on it is directly proportional to the magnitude and direction of the said force.
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.
Newton s second law of motion is related with the first law of motion.
Mathematical formulation of second law of motion.
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It gives the quantitative definition of force.
Let us say after a certain time t with a constant acceleration the final velocity becomes v.
Mathematical formulation of newton s second law of motion.
This means that the object will continue moving with uniform velocity u throughout the time t.
To v in the interval of time t this means initial velocity of the object u.
The final momentum p 2 m v.
Final velocity of the object v.
We can also measure force concerning mass and acceleration based on this law.
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That is when f 0 v u for whatever time t is taken.
Mathematical formulation of the second law of motion.
We know that momentum p mass x velocity.
Let the velocity of the object changes from u.
Let mass of an moving object m.
Mathematical formulation of second law of motion.
Here we see that the initial momentum p 2 m u.
Mathematical formulation of second law of motion.
Mathematical formulation of second law of motion we often observe that if the same magnitude of the force is used to push two blocks of wood where one of the blocks is heavier than the other the rate of change of position of the lighter block will be more than the heavier ones.
Mathematically it describes the causes and effects of force and changes in motion of an object.
Mathematical formulation of second law of motion.
Before understanding the equation of newton s second law of motion which deals with force mass and acceleration of an object let.
Now newton s second law of motion can be mathematically represented asyou know that using this.