drive the equation v =u+at
Answers
Answer :-
- Derivation of Equation of Motions
Now let's start the derivation with the first equation of motion i.e. v=u+at where u is the initial velocity, v is the final velocity and a is the constant acceleration.
Assuming that a body started with initial velocity “u” and after time t it acquires final velocity v due to uniform acceleration a.
We know acceleration is defined as the rate of change of velocity, also which is given by slope of the velocity time graph.
Thus both from definition as well as graph
Acceleration = Change in velocity/Time Taken i.e. a = v-u /t or at = v-u
Therefore,
we have: v = u + at
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☆ derive the equation v = u + at
V = final velocity
u = initial velocity
a = acceleration
t = time taken
B
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A |----------------------| D v
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O [ time ] C
let us consider an object moving with initial velocity ( u ) after time ( t ) it attains final velocity ( v ) covering distance ( s ) with uniform acceleration ( a ) .
OA = u
BC = V
BD = [ BC - DC = BD ]
BD = [ u - v = BD ]
OC = t
acceleration = change of velocity
time taken
a = BC - DC
OC
a = BD
t
a = v - u [ take (t) to right hand side ]
t
at = v - u [ take (u) to right hand side ]
u + at = v
v = u + at
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