derive three equations of motion from newton's second law
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Hello dear,
◆ Newton's second law of motion-
It states that net force acting on a body is directly proportional to mass and acceleration.
F = ma
◆ Derivation-
Let,
s = displacement
t = time interval
u = initial velocity
v = final velocity
a = acceleration
As we know,
a = dv/dt
a = (v-u)/t
at = v-u
v = u + at ...(1)
Average velocity is calculated with-
vavg = (u+v)/2
s/t = (u+u+at)/2
s/t = u + 1/2 at
s = ut + 1/2 at^2 ...(2)
We can multiply vavg with a,
vavg×a = (u+v)/2 × (v-u)/t
as/t = (v^2-u^2)/2t
2as = v^2-u^2
v^2 = u^2 + 2as ...(3)
Hence, proved.
Hope this helps...
◆ Newton's second law of motion-
It states that net force acting on a body is directly proportional to mass and acceleration.
F = ma
◆ Derivation-
Let,
s = displacement
t = time interval
u = initial velocity
v = final velocity
a = acceleration
As we know,
a = dv/dt
a = (v-u)/t
at = v-u
v = u + at ...(1)
Average velocity is calculated with-
vavg = (u+v)/2
s/t = (u+u+at)/2
s/t = u + 1/2 at
s = ut + 1/2 at^2 ...(2)
We can multiply vavg with a,
vavg×a = (u+v)/2 × (v-u)/t
as/t = (v^2-u^2)/2t
2as = v^2-u^2
v^2 = u^2 + 2as ...(3)
Hence, proved.
Hope this helps...
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