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 velocity is increased three times.​

Answer 1

Answer :-

$\:\\\large{\boxed{\sf{Firstly,\;let's\;understand\;the\;concept\;used\;:-}}}$

Here the concept ot Kinetic Energy has been used. We see that Kinetic Energy is the half of product of mass and velocity square. Firstly, we can find the mass of the from the equation of Kinetic Energy and then we can can apply that into the new equation where there is thrice of kinetic energy.

Let's do it !!

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★ Formula Used :-

$\:\\\large{\boxed{\sf{i.)\;\;\;Kinetic\;Energy\;=\;\bf{\dfrac{1}{2}\:\times\:m\:\times\:v^{2}}}}}$

$\:\\\large{\boxed{\sf{ii.)\;\;\;Kinetic\;Energy\;=\;\bf{\dfrac{1}{2}\:\times\:m\:\times\:(3\:\times\:v)^{2}}}}}$

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★ 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 velocity is increased three times.

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★ Solution :-

Given,

» Kinetic Energy of the body = 25 Joules

» Velocity of the body = 5 m/sec

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~ For the mass of the body :-

$\:\\\qquad \large{\sf{:\longrightarrow\;\;\;Kinetic\;Energy\;=\;\bf{\dfrac{1}{2}\:\times\:m\:\times\:v^{2}}}}$

$\:\\\qquad \large{\sf{:\longrightarrow\;\;\;25\;=\;\bf{\dfrac{1}{2}\:\times\:m\:\times\:(5)^{2}}}}$

$\:\\\qquad \large{\sf{:\longrightarrow\;\;\;25\;=\;\bf{\dfrac{1}{2}\:\times\:m\:\times\:25}}}$

$\:\\\qquad \large{\sf{:\longrightarrow\;\;\;m\;=\;\bf{\dfrac{2}{1}\:\times\:\dfrac{25}{25}\:\;=\:\;\underline{\underline{2\;\;Kg}}}}}$

$\:\\\large{\boxed{\boxed{\tt{Hence,\;\;mass\;\;of\;\;the\;\;object\;\;is\;\;\boxed{\bf{2\;\;Kg}}}}}}$

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~ For the Kinetic Energy of the body when velocity is three times :-

$\:\\\qquad \large{\sf{:\longrightarrow\;\;\;Kinetic\;Energy\;=\;\bf{\dfrac{1}{2}\:\times\:m\:\times\:3\:\times\:v^{2}}}}$

$\:\\\qquad \large{\sf{:\longrightarrow\;\;\;Kinetic\;Energy\;=\;\bf{\dfrac{1}{2}\:\times\:2\:\times\:(3\:\times\:5)^{2}}}}$

$\:\\\qquad \large{\sf{:\longrightarrow\;\;\;Kinetic\;Energy\;=\;\bf{\dfrac{1}{2}\:\times\:2\:\times\:(15)^{2}}}}$

$\:\\\qquad \large{\sf{:\longrightarrow\;\;\;Kinetic\;Energy\;=\;\bf{1\times\:225\;\;=\;\;\underline{\underline{225\;\;Joules}}}}}$

$\:\\\large{\underline{\underline{\rm{Thus,\;kinetic\;energy\;of\;the\;body\;when\;velocity\;is\;3\;times\;is\;\;\boxed{\bf{225\;\;Joules}}}}}}$

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★ More formulas to know :-

$\:\\\sf{\leadsto\;\;\;Potential\;Energy\;=\;mgh}$

$\:\\\sf{\leadsto\;\;\;Heat\;Energy\;=\;Force\:\times\:Distance}$

$\:\\\sf{\leadsto\;\;\;Power\;=\;\:\dfrac{Work}{Time}}$

$\:\\\sf{\leadsto\;\;\;Pressure\;=\;\:\dfrac{Force}{Area}}$

$\:\\\sf{\leadsto\;\;\;Stress\;=\;\:\dfrac{Force}{Area}}$

$\:\\\sf{\leadsto\;\;\;Strain\;=\;\:\dfrac{Change\:in\:Dimension}{Original\:Dimension}}$

$\:\\\sf{\leadsto\;\;\;Coefficient\;of\;Elasticity\;=\;\:\dfrac{Stress}{Strain}}$

$\:\\\sf{\leadsto\;\;\;Impulse\;of\;Force\;=\;Force\:\times\:Time}$

$\:\\\sf{\leadsto\;\;\;Coefficient\;of\;Viscosity\;=\;\dfrac{Force\:\times\:Distance}{Area\:\times\:Velocity}}$

$\:\\\sf{\leadsto\;\;\;Pressure\;Gradient\;=\;\:\dfrac{Pressure}{Distance}}$

$\:\\\sf{\leadsto\;\;\;Force\;Constant\;=\;\:\dfrac{Force}{Displacement}}$

$\:\\\sf{\leadsto\;\;\;Velocity\;Gradient\;=\;\:\dfrac{Velocity}{Distance}}$

Answer 2

Given:

• Kinetic energy of an object of mass m = 25J
• Object velocity , v = 5 m/s

To Find :

The Kinetic energy when object velocity is increased three times .

Solution :

Let the intital kinetic energy of object be $\sf\:K_1=25J$ and initial velocity $\sf\:v_1=v=5ms^{-1}$

and $\sf\:k_2$ be kinetic energy of an object when it's Velocity $\sf\:v_2=3v_1=15ms^{-1}$

Initial Kinetic energy

$\rm\:K_1=\dfrac{1}{2}m(v_1)^2$

$\sf\implies\:K_1=\dfrac{1}{2}mv^2..(1)$

Kinetic energy when Velocity increase three times

$\rm\:K_2=\dfrac{1}{2}m(v_2)^2$

$\sf\implies\:K_2=\dfrac{1}{2}m(3v)^2..(2)$

Now ,

Divide Equation (1) & (2)

$\sf\dfrac{K_1}{K_2}=\dfrac{\frac{1}{2}mv^2}{\frac{1}{2}m(3v)^2}$

$\sf\implies\dfrac{K_1}{K_2}=\dfrac{1}{9}$

$\sf\implies\dfrac{25}{K_2}=\dfrac{1}{9}$

$\sf\implies\:K_2=25\times9$

$\sf\implies\:K_2=225J$