derive kinematic equations of motion using the method of calculus where acceleration of a body is constant
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By using calculus
1). Acceleration is given as rate of change of velocity
a= dt/dv
Now on integrating both sides
a∫
0
t
dt=∫
u
v
dv
On solving the above we get
v=u+at
2). Rate of the displacement is equal to velocity
v=
dt
ds
On integrating the above equation we get
∫
0
s
ds=v∫
0
t
dt
On substituting the value ofv=u+at
We get
s=ut+
2
1
at
2
3). Distance travelled is equal to average speed time time
s=
2
u+v
t
By using the first equation and substituting the value oft=
a
v−u
We get
v
2
=u
2
+2as
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