Question

The kinetic energy of an object of mass m, moving with a velocity of 5 m/s is 25 J. What will be its kinetic energy when its speed is doubled? it is given here doubled not tripled​

Answer 1

⇝Given :)

• Initial Velocity = 5 m/s
• Kinetic energy = 25 J
• Its speed is doubled .

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⇝To Find :)

• Find kinetic energy when speed is doubled .

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⇝Formula Used :)

Kinetic Energy :-

${\large{\orange{\bigstar \: \: {\blue{\underbrace{\underline{\orange{\bf{K.E = \frac{1}{2} \times m {v}^{2} }}}}}}}}}$

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⇝Solution :)

${\green{❒}}{\underline{\bf{ First ,finding \: the \: mass :}}}$

${\large{:{\longmapsto{\bf{K.E = \frac{1}{2} \times m {v}^{2} }}}}}$

${\large{:{\longmapsto{\bf{25 = \frac{1}{2} \times m \times {5}^{2} }}}}}$

${\large{:{\longmapsto{\bf{25 = \frac{1}{2} \times m \times25 }}}}}$

${\large{:{\longmapsto{\bf{25 \times 2 = 1 \times m \times 25 }}}}}$

${\large{:{\longmapsto{\bf{50 = m \times 25 }}}}}$

${\large{:{\longmapsto{\bf{M ={\cancel \frac{50}{25} }}}}}}$

${\large{\purple{:{\longmapsto{\overline{\underline{\boxed{\bf{Mass = 2 \: kg}}}}}}}}}$

${\pink{❒}}{\underline{\bf{ Than, \: K.E \: if \: speed \: is \: doubled:}}}$

Doubled Speed = 5 × 2 = 10 m/s

Mass = 2kg

Kinetic Energy = ?

${\large{:{\longmapsto{\bf{K.E = \frac{1}{2} \times m {v}^{2} }}}}}$

${\large{:{\longmapsto{\bf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{1}{2} \times 2 \times {10}^{2} }}}}}$

${\large{:{\longmapsto{\bf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{1}{2} \times 2 \times100 }}}}}$

${\large{:{\longmapsto{\bf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{1}{2} \times 200 }}}}}$

${\large{:{\longmapsto{\bf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{1}{\cancel{2}} \times{\cancel{ 200}} }}}}}$

${\large{\purple{:{\longmapsto{\overline{\underline{\boxed{\bf{K.E = 100 \: Joules}}}}}}}}}$

${\orange{✧}}{\underline{\bf{ Therefore :}}}$

${\pmb{\blue{\underline{\orange{\underline{\red{\mathfrak{New \: Kinetic \: Energy = 100 \: Joules}}}}}}}}$

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• @Okhey