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1.) Newton's second law, which states that the force F acting on a body is equal to the mass m of the body multiplied by the acceleration a of its centre of mass, F = ma, is the basic equation of motion in classical mechanics.
Force, F = Mass, m × Acceleration, a
➡ F = ma
The three general equations of motion are :
➡ v = u + at
➡ s = ut + (1/2) × at^2
➡ v^2 = u^2 + 2as
2.) First general equation of motion :
v = u + at
Derivation :-
Let consider a body moving with initial velocity u, constant acceleration a, time t and final velocity v.
Then,
We know that,
Acceleration = Change of velocity/Time taken
➡ a = (v - u) /t
➡ at = v - u
➡v = u + at
Hence, derived.
3.) Third equation of motion :
S = ut + 1/2 × at^2
Derivation :-
Let the Displacement covered by the body be 'S' whose initial velocity is 'u', final velocity is 'v' and time taken is 't'.
Then, given,
➡ Displacement = S
➡ Initial Velocity = u
➡ Final Velocity = v
➡ Time taken = t
We know that,
Displacement = Average Velocity × Time ....... (i)
And, Average Velocity = (Initial Velocity + Final Velocity) / 2 ....... (ii)
By applying the values, of equation (ii) in equation (i), we get,
➡ Displacement = {(Initial Velocity + Final Velocity) / 2} × t
Let us apply now the symbols of this equation,
➡ S = { (u + v) / 2 } × t
..... (iii)
First equation of motion :
v = u + at
By applying the value 'v' from the First of equation of motion in the equation (iii), we get,
➡ S = { (u + u + at) / 2 } × t
➡ S = { (2u + at) / 2 } × t
➡ S = [ (2u / 2) + (at / 2) ] × t
➡ S = [ u + (at / 2) ] × t
➡ S = ut + (at^2) / 2
➡ S = ut + (1/2) × at^2
In this way, we derive the third equation of motion.
Hence, proved.
4.)
➡ The principle is that the slope of the line on a velocity-time graph reveals useful information about the acceleration of the object. If the acceleration is zero, then the slope is zero (i.e., a horizontal line). If the acceleration is positive, then the slope is positive (i.e., an upward sloping line).
➡ Velocity-time graphs are used to describe the motion of objects which are moving in a straight line. They can be used to show acceleration and to work out displacement.
➡ The slope of a velocity graph represents the acceleration of the object. So, the value of the slope at a particular time represents the acceleration of the object at that instant.
Answer:
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