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pushpakRuhil
@pushpakRuhil
August 2021
2
22
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prove the 3 equations of motion
using calculus.
Answers & Comments
vishal244
v²= u²+2as
Actually I don't know how to derive it. But here is some hints are provided.
You want it by integration.(v² - u²) /2 indicates the integration of v dv limit u to v.
Here is the proof -
a= dv/dt……1
v=ds/dt……….2
from 1 & 2:
a ds/dt = v dv/ dt
implies a ds =v dv
after integration you will get 3rd equation.
1 votes
Thanks 1
Khushib707
First equation of motion:
Consider a body having initial velocity u,If it is subjected to an acceleration 'a' so that after time 't' its velocity becomes v.
By the definition of acceleration
acceleration=Change in velocity/time taken
a=(v-u)/t
v=u+at
Second equation of motion:
Suppose the distance travelled by the above body in time t=s
we have average velocity=(Initial velocity+Final velocity)/2
average velocity =u+v/2
distance travelled =average velocity / time
s=v+u/2*t
using v=u+at in the above equation.
s=u+at+u/2*t
s=2ut+at²/2
s=ut+1/2at²
Third equation of motion:
using first equation of motion..
s=v+u*t/2
s=[v+u][v-u]/2a
s=v²-u²/2
2as=v²-u²
v²=u²+2as
i hope u find this answer helpful...
mark it as brainilist...
0 votes
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Answers & Comments
v²= u²+2as
Actually I don't know how to derive it. But here is some hints are provided.
You want it by integration.(v² - u²) /2 indicates the integration of v dv limit u to v.
Here is the proof -
a= dv/dt……1
v=ds/dt……….2
from 1 & 2:
a ds/dt = v dv/ dt
implies a ds =v dv
after integration you will get 3rd equation.
Consider a body having initial velocity u,If it is subjected to an acceleration 'a' so that after time 't' its velocity becomes v.
By the definition of acceleration
acceleration=Change in velocity/time taken
a=(v-u)/t
v=u+at
Second equation of motion:
Suppose the distance travelled by the above body in time t=s
we have average velocity=(Initial velocity+Final velocity)/2
average velocity =u+v/2
distance travelled =average velocity / time
s=v+u/2*t
using v=u+at in the above equation.
s=u+at+u/2*t
s=2ut+at²/2
s=ut+1/2at²
Third equation of motion:
using first equation of motion..
s=v+u*t/2
s=[v+u][v-u]/2a
s=v²-u²/2
2as=v²-u²
v²=u²+2as
i hope u find this answer helpful...
mark it as brainilist...