Question

The Velocity of a body of mass 60 kg reaches 15 m/s from 0 m/s in 12 second Calculate the kE​ and power of the body

Answer 1

$\sf Given \begin {cases} & \sf { Mass \: = m = \: 60\: kg } \\ & \sf{ Initial \: Velocity = u = \: 0m/s} \\ &\sf { Final\: Velocity = v = 15m/s } \\ & \sf{ Time = t = 12sec } \end {cases}$

⠀⠀⠀⠀

$\sf To \: find \begin {cases} & \sf { Kinetic \: Energy \: = K.E. \: = \: ?? } \\ &\sf{ Power = ?? } \\ \end {cases}$

⠀⠀⠀⠀

We know that :-

⠀⠀⠀⠀

$\star\;{\boxed{\sf{\pink{Kinetic \: Energy ( KE ) = \dfrac{1}{2} \times Mass ( M ) \times [ Final \: Velocity ( v ) \: - \: Initial \: Velocity \: ( u ) ] ^2 }}}}$

⠀⠀⠀⠀

$:\implies\sf KE = \dfrac{1}{2} \times 60 \times [ 15 - 0 ]^2$

⠀⠀⠀⠀

$:\implies\sf KE = \dfrac{1}{2} \times 60 \times 15^2$

⠀⠀⠀⠀

$:\implies\sf KE = 30 \times 15 ^2$

⠀⠀⠀⠀

$:\implies\sf KE = 30 \times 225$

⠀⠀⠀⠀

$:\implies\sf KE = 6750 Joules$

⠀⠀⠀⠀

$:\implies{\underline{\boxed{\frak{\purple{ Kinetic \: Energy \: = 6750 \: joules \: }}}}}\;\bigstar$

⠀⠀

⠀⠀⠀⠀

Now ;

⠀⠀⠀⠀

$\star\;{\boxed{\sf{\pink{Power ( P ) = \dfrac{Energy }{Time ( t ) } }}}}$

⠀⠀⠀⠀

$:\implies\sf Power = \dfrac{6750}{12}$

⠀⠀⠀⠀

$:\implies\sf Power = \dfrac{3375}{6}$

⠀⠀⠀⠀

$:\implies\sf Power = \dfrac{1125}{2}$

⠀⠀⠀

$:\implies\sf Power = 562.5 watt$

⠀⠀⠀⠀

$:\implies{\underline{\boxed{\frak{\purple{ Power \: = 562.5 \: watt \: }}}}}\;\bigstar$

⠀⠀⠀⠀

⠀⠀⠀⠀

$\therefore\:{\underline{\sf{Power \; of \; the \; body \: is \; \bf{ 562.5\: watt }.}}}$

⠀⠀

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

Answer 2

Given :-

Mass = 60 kg

Initial velocity = 0 m/s

Final velocity = 15 m/s

Time = 12 second

To Find :-

KE

Power

Solution :-

We know that

$\bf KE = \dfrac{1}{2}mv^2 - \dfrac{1}{2} mu^2$

$\sf KE = \dfrac{1}{2}m\bigg(v^2-u^2\bigg)$

$\sf KE = \dfrac{1}{2} \times 60\bigg(15^2 - 0^2\bigg)$

$\sf KE = \dfrac{1}{2} \times 60 \bigg(225 - 0\bigg)$

$\sf KE = 30 \times 225$

$\mathfrak{ KE = 6750 \; joules}$

$\mathfrak{Power = \dfrac{Energy}{Time}}$

$\sf Power = \dfrac{6750}{12}$

$\sf Power = 562.5 \; Watts$