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
• K.E,i = 25J
• Speed is doubled

To Find

• Ke,f = ?

Solution

☯ K.E = ½mv²

• Here we shall first find the mass of the body with the values given initially, then substitute the mass and with speed as 10 m/s find the final K.E

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✭ According to the Question :

➞ K.E = ½mv²

➞ 25 = ½ × m × 5²

➞ 25 × 2 = 25m

➞ 50/25 = m

➞ m = 2 kg

So then if the speed is doubled,

• K.E = ½mv² = ½ × 2 × 10²
• K.E,f = 100 J

Answer 2

⇝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 :

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

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⇝Solution :-

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

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

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

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

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

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

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

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

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

• Doubled Speed = 5 × 2 = 10 m/s
• Mass = 2kg
• Kinetic Energy = ?

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

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

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

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

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

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

${\red{❒}}{\underline{\bf{ Therefore :}}}$

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

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