Question

✦✧✧ Question ✧✧✦ ➠ ᴅᴏɴᴛ sᴘᴀᴍ⚠️ 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,

velocity of object,$\bf{v=5\: m/s}$

As kinetic energy of the object is,

$\bf{E_k =25\:J}$

$\bf\red{ E_k=\dfrac{1}{2}{mv^2}}$

$\implies 25 = \dfrac{1}{2}\times m\times 5^2$

$\implies m = \dfrac{50}{25}$

$\large \implies \bf \pink{ m = 2\: kg}$

Now,

When the velocity is Doubled,

so new velocity is 10 m/s

Hence

$E_k=\dfrac{1}{2}\times 2\times 10^2$

$= \dfrac{200}{2}$

$\large \implies \bf \pink{ E_k = 100\: Joule}$

Answer 2

$\large \dag$ 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 ?

$\large \dag$ Answer :-

$\red\dashrightarrow\underline{\underline{\sf  \green{Kinetic\:Energy   \:  is \:  100\: Joule}} }$

$\large \dag$ Step by step Explanation :-

Here we have given that,

• Velocity of Object = v = 5 m/s

• Kinetic Energy of Object = K.E. = 25 J

• Mass of Object = m

We Know that Kinetic energy is ;

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

⏩ Putting Values we get ,

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

$:\longmapsto \rm 25 = \frac{25}{2} \times m$

$:\longmapsto \rm m = \cancel{25} \times \frac{2}{ \cancel{25}}$

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

❒ When it's speed is doubled :-

$:\longmapsto \rm Velocity = v' = 2 \times 5$

$\pink{ \large :\longmapsto  \underline {\underline{{\bf v' = 10 \: m/s} }}}$

Now Applying Formula if Kinetic Energy ;

$:\longmapsto \rm K.E.' = \frac{1}{2} \times m \times ( {v'})^{2}$

$:\longmapsto \rm K.E.' = \frac{1}{\cancel2} \times \cancel2 \times {10}^{2}$

$:\longmapsto \rm K.E.' = 10 \times 10$

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

Therefore,

$\large\underline{\pink{\underline{\frak{\pmb{Kinetic \: Energ \text y \: is \: 100 \: Joule}}}}}$