The acceleration ‘a’ of a particle starting from rest varies with time according to relation a = αt + β. Find the velocity of the particle after a time ‘t’.
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Answered by
43
we know ,
acceleration is rate of change of velocity . mathematically acceleration = ∆v/∆t
where ∆v = ( final velocity - inital velocity)
∆t = time taken by particle.
if we talk about very small change in velocity and time , then we take
acceleration (a) = dv/dt
now, a/c to question ,
a = αt + β
dv/dt = αt + β
dv = αt.dt + β.dt
now integrate
Vf - Vi = αt²/2 + βt
but particle starts from rest so, Vi = 0
hence,
Vf = αt²/2 + βt
acceleration is rate of change of velocity . mathematically acceleration = ∆v/∆t
where ∆v = ( final velocity - inital velocity)
∆t = time taken by particle.
if we talk about very small change in velocity and time , then we take
acceleration (a) = dv/dt
now, a/c to question ,
a = αt + β
dv/dt = αt + β
dv = αt.dt + β.dt
now integrate
Vf - Vi = αt²/2 + βt
but particle starts from rest so, Vi = 0
hence,
Vf = αt²/2 + βt
Answered by
3
Answer:a= a=alpha×t^2/2+beta×t
Explanation:
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