Question

explain momentum . write the three laws of motion and derive as well as explain them .

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Answer 1

Momentum is a vector quantity that is the product of the mass and the velocity of an object or particle. The standard unit of momentum magnitude is the kilogram-meter per second (kg · m/s or kg · m · s -1 ). Alternatively, the gram-centimeter per second (g · cm/s or g · cm · s -1 ) can be used to express momentum magnitude. The direction of a momentum vector can be expressed in various ways, depending on the number of dimensions involved, and is the same as the direction of the velocity vector.
(1) First equation of Motion:

V = u + at
soln.
Consider a body of mass “m” having initial velocity “u”.Let after time “t” its final velocity becomes “v” due to uniform acceleration “a”.

Now we know that:
Acceleration = change in velocity/Time taken

=> Acceleration = Final velocity-Initial velocity / time taken

=> a = v-u /t
=>at = v-u

or v = u + at
This is the first equation of motion.
—————————————-
(2) Second equation of motion:
s = ut + 1/2 at^2

sol.
Let the distance travelled by the body be “s”.
We know that
Distance = Average velocity X Time

Also, Average velocity = (u+v)/2

.: Distance (t) = (u+v)/2 X t …….eq.(1)

Again we know that:
v = u + at
substituting this value of “v” in eq.(2), we get

s = (u+u+at)/2 x t
=>s = (2u+at)/2 X t
=>s = (2ut+at^2)/2
=>s = 2ut/2 + at^2/2

or s = ut +1/2 at^2

This is the 2nd equation of motion.
……………………………………………………………
(3) Third equation of Motion
v^2 = u^2 +2as

sol.
We know that
V = u + at
=> v-u = at
or t = (v-u)/a ………..eq.(3)

Also we know that
Distance = average velocity X Time
.: s = [(v+u)/2] X [(v-u)/a]
=> s = (v^2 – u^2)/2a

=>2as = v^2 – u^2

or v^2 = u^2 + 2as

This is the third equation of motion.