Question

${\large{\underline{\green{\bf{question : - }}}}}$
kinetic energy of an object of mass, m moving with a velocity of 5 ms 1 is 25 What will be its kinetic energy when its velocity is doubled? What will be its kine energy when its velocity is increased three times.


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please give correct answers ​

Answer 1

Answer:

kinetic energy of an object of mass, m moving with a velocity of 5 ms 1 is 25 What will be its kinetic energy when its velocity is doubled? What will be its kine energy when its velocity is increased three times.

______________________

please give correct answers

Answer 2

⇝Given :

• ➬ Kinetic energy of an object of mass m is moving with a velocity of 5 m/s¹ is 25.

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⇝To Find :

• ➬ Kinetic energy if speed of is doubled.
• ➬ Kinetic energy if velocity is increased 3 times.

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⇝Solution :

~ How to Solve :

By using the formula for Kinetic energy we will first calculate the mass of the object. And than after calculating the mass we can find the Kinetic energy if Velocity is doubled and velocity is tripled.

~ Formula Used :

$\large{\orange{\bigstar}} \: \: {\underline{\boxed{\red{\sf{ K.E = \dfrac{1}{2}mv²}}}}}$

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~ Calculating the Mass :

${\longmapsto{\qquad{\sf{ K.E = \dfrac{1}{2}mv²}}}} \\ \\ {\longmapsto{\qquad{\sf{ 25 = \dfrac{1}{2} \times m \times (5)² }}}} \\ \\{\longmapsto{\qquad{\sf{ \dfrac{1}{2} \times m = \dfrac{25}{25} }}}} \\ \\{\longmapsto{\qquad{\sf{ \dfrac{1}{2} \times m = \cancel\dfrac{25}{25} }}}} \\ \\{\longmapsto{\qquad{\sf{ 1 \times m = 1 \times 2}}}} \\ \\ {\sf{ Mass \: of \: object \: = {\green{\sf{ 2 \: kg}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━}$

~ Calculating the K.E if velocity is doubled :

Here :

• ➳ M = Mass = 2 kg
• ➳ V = Velocity = ${\sf{5 \times 2}}$ = 10 m/s¹
• ➳ K.E = Kinetic energy = ?

Calculation starts :

${\implies{\qquad{\sf{ K.E = \dfrac{1}{2}mv²}}}} \\ \\{\implies{\qquad{\sf{ K.E = \dfrac{1}{2} \times 2 \times (10)²}}}} \\ \\{\implies{\qquad{\sf{ K.E = \dfrac{1}{2} \times 2 \times 100}}}} \\ \\{\implies{\qquad{\sf{ K.E = \dfrac{1}{\cancel2} \times \cancel{200}}}}} \\ \\{\sf{ Kinetic \: Energy{\small_{(Doubled \: velocity ) }} = {\orange{\sf{ 100 \: J }}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━}$

~ Calculating the K.E If velocity is tripled :

Here :

• ➳ M = Mass = 2 kg
• ➳ V = Velocity = ${\sf{5 \times 3}}$ = 10 m/s¹
• ➳ K.E = Kinetic energy = ?

Calculation starts :

${\implies{\qquad{\sf{ K.E = \dfrac{1}{2}mv²}}}} \\ \\ {\implies{\qquad{\sf{ K.E = \dfrac{1}{2} \times 2 \times (15)²}}}} \\ \\{\implies{\qquad{\sf{ K.E = \dfrac{1}{2} \times 2 \times 225}}}} \\ \\{\implies{\qquad{\sf{ K.E = \dfrac{1}{\cancel2} \times \cancel{550}}}}} \\ \\{\sf{ Kinetic \: Energy{\small_{(Tripled \: velocity ) }} = {\color{darkblue}{\sf{ 225 \: J }}}}}$

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Therefore :

❝ Kinetic energy is 100 joules if velocity is doubled. ❞

❝ Kinetic energy is 225 Joules if velocity is tripled . ❞

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✬Know More :

3 equations of Motion :

$\begin{gathered}\pink{\large \qquad \boxed{\boxed{\begin{array}{cc} \ ➳ \: \: \bf {\color{maroon}{v = u + at}} \\ \\ \ ➳ \: \: \bf {\color{red}{s = ut + \dfrac{1}{2}g {t}^{2} }} \\ \\ \ ➳ \: \: \bf{\color{maroon}{{v}^{2} - {u}^{2} = 2as}} \end{array}}}}\end{gathered}$