A particle of mass $0.1 \,kg$ is subjected to a force which varies with distance as shown in fig. If it starts its journey from rest at $x = 0$, its velocity at $x = 12\,m$ is .......... $m/s$
A particle of mass $0.1 \,kg$ is subjected to a force which varies with distance as shown in fig. If it starts its journey from rest at $x = 0$, its velocity at $x = 12\,m$ is .......... $m/s$
$0$
$20\sqrt 2$
$20\sqrt 3 $
$40$
A particle of mass $0.1 \,kg$ is subjected to a force which varies with distance as shown in fig. If it starts its journey from rest at $x = 0$, its velocity at $x = 12\,m$ is .......... $m/s$
Area between curve and displacement axis
= $\frac{1}{2} \times (12 + 4) \times 10$ $= 80 J$
In this time body acquire kinetic energy = $\frac{1}{2}m{v^2}$
by the law of conservation of energy
$\frac{1}{2}m{v^2} = 80J$
$⇒$ $\frac{1}{2} \times 0.1 \times {v^2} = 80$
$⇒$ $v^2 = 1600$
$⇒$ $v = 40 m/s$
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