Can you tell all derivation of motion
Dear Student,
Let,
Acceleration = a
Displacement = s
Initial velocity = u
Final velocity = v
Time taken = t
The first equation of motion.
a = change in velocity / t
= v - u / t
Therefore ,
at = v - u
and, v = u + at
Second equation of motion
s = (average velocity ) t
= ( u + v / 2 ) t
= ( u + u +at /2 ) t [ v = u + at]
= ( 2 u + at / 2 ) t
= ( 2u/2 + at/2 ) / t
= ( u + at/ 2 ) t
= ut + 1/2 at2
Therefore,
s = ut + 1/2 at2
Third equation of motion
v = u + at
Therefore,
t = v - u / a............. (i)
s = ut + 1/2 at2
= u ( v - u /a) + a/2 ( v - u / a )2 ...[ from (i)]
Multiplying 2 on both sides of the equation , we get
2 * s = 2 * [u ( v - u ) a + a/2 ( v - u / a )2 ]
2s = 2u ( v - u )/a + a ( v - u / a )2
= ( 2uv - 2u2)/ a + a ( v2 + u2 - 2uv/ a2)
= ( 2uv - 2u2)/a + v2 + u2 - 2uv / a
= ( 2uv - 2u2 + v2 + u2 - 2uv) / a
Simplifying , we get
2as = v2- u2
Regards
Let,
Acceleration = a
Displacement = s
Initial velocity = u
Final velocity = v
Time taken = t
The first equation of motion.
a = change in velocity / t
= v - u / t
Therefore ,
at = v - u
and, v = u + at
Second equation of motion
s = (average velocity ) t
= ( u + v / 2 ) t
= ( u + u +at /2 ) t [ v = u + at]
= ( 2 u + at / 2 ) t
= ( 2u/2 + at/2 ) / t
= ( u + at/ 2 ) t
= ut + 1/2 at2
Therefore,
s = ut + 1/2 at2
Third equation of motion
v = u + at
Therefore,
t = v - u / a............. (i)
s = ut + 1/2 at2
= u ( v - u /a) + a/2 ( v - u / a )2 ...[ from (i)]
Multiplying 2 on both sides of the equation , we get
2 * s = 2 * [u ( v - u ) a + a/2 ( v - u / a )2 ]
2s = 2u ( v - u )/a + a ( v - u / a )2
= ( 2uv - 2u2)/ a + a ( v2 + u2 - 2uv/ a2)
= ( 2uv - 2u2)/a + v2 + u2 - 2uv / a
= ( 2uv - 2u2 + v2 + u2 - 2uv) / a
Simplifying , we get
2as = v2- u2
Regards