A particle starting from rest under...
Question
A particle starting from rest undergoes a rectilinear motion with acceleration a. The variation of a with time t is shown below. The maximum velocity attained by the
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A particle starting from rest undergoes a rectilinear motion with acceleration a. The variation of a with time ( t ) is shown below. The maximum velocity attained by the particle during its motion is

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Physics
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A particle starting from rest undergoes a rectilinear motion with acceleration a. The variation of a with time t is shown below. The maximum velocity attained by the particle during its motion is
Fullscreen

From the diagram we can expless equation as
[
a=10-left(frac{10}{12}right) t
]
where at ( t=0 ) as ( 10 mathrm{m} / mathrm{s}^{2}, t=12 ) a ( =0 mathrm{m} / mathrm{s}^{2} )
by integration we get
[
begin{array}{l}
int a=int 10-left(frac{0}{12}right) t
V=10 t-left(frac{10}{12}right) frac{t^{2}}{2}
V=10 t-frac{5 t^{2}}{12}
end{array}
]
fol ( operatorname{Vmax} frac{d v}{d t}=0 )
[
begin{array}{l}
Rightarrow frac{d V}{d t}=10-frac{5}{12} times 2 times t
0=10-frac{5 t}{6} Rightarrow frac{1}{6}=100-1 t=12 mathrm{sec}
end{array}
]
Volocity at 12 sec
[
V=(10 times 12)-frac{5}{12} times 12 times 12
]
[
V=120-60=60 mathrm{m} / mathrm{s}
]
Vmax
[
text { Areaculdergraph }=frac{1}{2} times 12 times 10=60 mathrm{m} / mathrm{s}
]

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