Question

a kibetic energy of mass 4 kg is 40 j. its speed is

Answer 1

${\large{\pmb{\sf{\underline{Required \: solution...}}}}}$

${\bigstar \:{\pmb{\sf{\underline{Correct \: question...}}}}}$

⋆ The kinetic energy of mass 4 kg is 40 J. It's speed is……

${\bigstar \:{\pmb{\sf{\underline{Given \: that...}}}}}$

⋆ Mass of a body is 4 kg

⋆ Kinetic energy of body is 40 Joules

${\bigstar \:{\pmb{\sf{\underline{To \: find...}}}}}$

⋆ Speed of the body

${\bigstar \:{\pmb{\sf{\underline{Solution...}}}}}$

⋆ Speed of the body = 4.47 m/s

${\bigstar \:{\pmb{\sf{\underline{Using \: concept...}}}}}$

⋆ Formula to find out the kinetic energy

${\bigstar \:{\pmb{\sf{\underline{Using \: formula...}}}}}$

${\sf{\star \: E_k \: = \dfrac{1}{2} (m)(v)^{2}}}$

${\bigstar \:{\pmb{\sf{\underline{Where...}}}}}$

⋆ m denotes mass

⋆ v denotes velocity or speed

${\sf{\star \: E_k \: denotes \: kinetic \: energy}}$

${\bigstar \:{\pmb{\sf{\underline{Full \; Solution...}}}}}$

~ To solve this question we just have to put the values according to the formula and have to solve. Using formula is of kinetic energy. Let's do it!

$\Rightarrow \rm E_k \: = \dfrac{1}{2} (m)(v)^{2} \\ \\ \Rightarrow \rm 40 \: = \dfrac{1}{2} (4) (v)^{2} \\ \\ \Rightarrow \rm 40 \: = \dfrac{1}{\cancel{{2}}} \cancel{(4)} (v)^{2} \\ \\ \Rightarrow \rm 40 \: = 2 (v)^{2} \\ \\ \Rightarrow \rm \dfrac{40}{2} \: = (v)^{2} \\ \\ \Rightarrow \rm \cancel{\dfrac{40}{2}} \: = (v)^{2} \\ \\ \Rightarrow \rm 20 \: = (v)^{2} \\ \\ \Rightarrow \rm \sqrt{20} \: = v \\ \\ \Rightarrow \rm 4.47 \: = v \\ \\ \Rightarrow \rm v \: = 4.47 \\ \\ \Rightarrow \rm Velocity \: = 4.47 \: m/s$

${\bigstar \:{\pmb{\sf{\underline{Verification...}}}}}$

~ Let us verify our question, by using formula to find the kinetic energy.

$\Rightarrow \rm E_k \: = \dfrac{1}{2} (m)(v)^{2} \\ \\ \Rightarrow \rm E_k \: = \dfrac{1}{2} (4) (4.47)^{2} \\ \\ \Rightarrow \rm E_k \: = \dfrac{4}{2} (4.47)^{2} \\ \\ \Rightarrow \rm E_k \: = \cancel{\dfrac{4}{2}} (4.47)^{2} \\ \\ \Rightarrow \rm E_k \: = 2(4.47)^{2} \\ \\ \Rightarrow \rm E_k \: = 2 \times 4.47 \times 4.47 \\ \\ \Rightarrow \rm E_k \: = 8.94 \times 4.47 \\ \\ \Rightarrow \rm E_k \: = 39.9618 \\ \\ \Rightarrow \rm E_k \: \approx 40 \: Joules \\ \\ {\pmb{\tt{Henceforth, \: verified!}}}$