Question

The Kinetic energy of an object
of mass, in moving with a velocity of 5ms-1 is 25 J. What will be its kinitic energy when
its velocity is doubled ? what will be its kinitic energy when its velocity is increased three times ?
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Answer 1

$\large{\underline{\underline{\mathrm{\blue{Question-}}}}}$

The Kinetic energy of an object of mass m, in moving with a velocity of 5 m/s is 25 J. What will be its kinitic energy when its velocity is doubled ? what will be its kinitic energy when its velocity is increased three times?

$\large{\underline{\underline{\mathrm{\blue{Answer-}}}}}$

★ When velocity is doubled, kinetic energy becomes 100 J.

★ When velocity is doubled, kinetic energy becomes 225 J.

$\large{\underline{\underline{\mathrm{\red{Explanation-}}}}}$

$\begin{lgathered}\bold{Given} \begin{cases}\sf{Kinetic\:energy\:=\:25\:J} \\ \sf{Velocity\:=\:5\:m/s}\\ \sf{mass\:=\:m}\end{cases}\end{lgathered}$

To find :

• Kinetic energy when velocity is doubled
• Kinetic energy when velocity is increased three times.

Solution :

We know that,

$\large{\boxed{\rm{\red{Kinetic\:Energy\:=\:\dfrac{1}{2}\:mv^2}}}}$

★ putting the given values,

$\mapsto$ $\rm{25\:=\:\dfrac{1}{2}\:m\:(5)^2}$

$\mapsto$ $\rm{25\:=\:\dfrac{1}{2}\:m\:25}$

$\mapsto$ m = 2 kg.

★ $\bold{\underline{\rm{\green{When\:velocity\:is\:doubled-}}}}$

Put Velocity = 5 × 2 => 10 m/s

$\rm{Kinetic\:energy\:=\:\dfrac{1}{\cancel{2}}\:\times\:\cancel{2}\:\times\:(10)^2}$

$\mapsto$ $\rm{Kinetic\:energy\:=\:100\:J}$

$\therefore$ When velocity is doubled, kinetic energy becomes 100 J.

★ $\bold{\underline{\rm{\green{When\:velocity\:increases\:three\:times-}}}}$

Put velocity = 5 × 3 => 15 m/s

$\rm{Kinetic\:energy\:=\:\dfrac{1}{\cancel{2}}\:\times\:\cancel{2}\:\times\:(15)^2}$

$\mapsto$ $\rm{Kinetic\:energy\:=\:225\:J}$

$\therefore$ When velocity is doubled, kinetic energy becomes 225 J.

Answer 2

$\huge\star{\green{\underline{\mathfrak{Answer :-}}}}$

$\bf{Given}\begin{cases}\sf{Kinetic\:energy\:of\:the\:object = 25 \:J}\\\sf{Velocity = 5 m{s}^{-1}}\\ \end{cases}$

$\bf{To\:Find}\begin{cases}\sf{K.E.\:when\:velocity\:is\:doubled}\\\sf{K.E.\:when\:velocity\:tripled}\\ \end{cases}$

$\bf {SOLUTION :-}$

We know that,

$\huge {\boxed {\tt K.E. = \dfrac {1}{2}m {v}^{2}}}$

So,

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

$\hookrightarrow {\tt 25 = \dfrac {1}{2}m \times 25}}$

$\hookrightarrow {\tt 1 = \dfrac {1}{2}m }}$

$\hookrightarrow {\tt m = 2\:kg}}$

WHEN VELOCITY IS DOUBLED,

So, v = 5 × 2 = 10 m/s

$\hookrightarrow \tt \therefore {K.E. =\dfrac {1}{\cancel {2}}\times \cancel {2}\times {10}^{2}}$

$\hookrightarrow \tt \therefore {K.E. = 100\:J}$

WHEN VELOCITY IS TRIPLED,

So, v = 5 × 3 = 15 m/s

$\hookrightarrow \therefore {\tt {K.E. =\dfrac {1}{\cancel {2}}\times \cancel{2} \times {15}^{2}}}$

$\hookrightarrow \tt \therefore {K.E. = 225\:J}$

$\rule{200}2$

$\huge {\tt KINETIC\:ENERGY\: :-}$

It is the energy of an object possessed during motion.

$\huge {\boxed {\tt K.E. = \dfrac {1}{2}m {v}^{2}}}$

$\huge {\tt POTENTIAL\:ENERGY\: :-}$

It is the energy stored in the object.

$\huge {\boxed {\tt P.E. = mgh}}$

$\rule{200}2$