Question

derive three equation of motion mathematically​

Answer 1

Step-by-step explanation:

Let us begin with the first equation, v=u+at. This equation only talks about the acceleration, time, the initial and the final velocity. Let us assume a body that has a mass “m” and 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

Therefore,  Acceleration = (Final Velocity-Initial Velocity) / Time Taken

Hence, a = v-u /t or at = v-u

Therefore, we have: v = u + at

v² = u² + 2as

We have, v = u + at. Hence, we can write t = (v-u)/a

Also, we know that, Distance = average velocity × Time

Therefore, for constant acceleration we can write: Average velocity = (final velocity + initial velocty)/2 = (v+u)/2

Hence, Distance (s) = [(v+u)/2]  × [(v-u)/a]

or  s = (v² – u²)/2a

or 2as = v² – u²

or v² = u² + 2as

s = ut + ½at²

Let the distance be “s”. We know that

Distance = Average velocity × Time. Also, Average velocity = (u+v)/2

Therefore, Distance (s) = (u+v)/2 × t

Also, from v = u + at, we have:

s = (u+u+at)/2 × t = (2u+at)/2 × t

s = (2ut+at²)/2 = 2ut/2 + at²/2

or s = ut +½ at²

Answer 2

Answer:

The first equation: Every object either in rest or uniform motion continues to be in that state until and unless an external unbalanced force acts upon it.

The second law:The rate of change of momentum of any body is directly proportional to applied force in the same direction.

The third law: For every action there is an equal and opposite reaction

Step-by-step explanation:

For second law..

for a body under the action of force F for time dt with mass m and velocity v ... we have p=mv and change is ∆p=m∆v

therefore by second law F is directly proportional to dp/dt ..

so F=k. dp/dt(k=some constant)

as p=mv and thus

F=d/dt (mv)

and as dv/dt = a (a=acceleration)

so we have

F=k.ma

taking k=1

F=ma. (a=acceleration)

For 3rd law

Let us consider two bodies A and B having mass m1 and m2 . Let them colloid and then the forces can be

force on A by B =F(AB)

force on B by A =F(BA)

so by third law

F(AB)= -F(AB)

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