If a particle starting from rest is moving with a uniform acceleration of 10ms power minus 2 ,then the final velocity when it cove

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1. [tex]{\large{\pmb{\sf{\underline{RequirEd \: Solution…}}}}}[/tex]

   [tex]{\bigstar \:{\pmb{\sf{\underline{Understanding \: the \: question…}}}}}[/tex]

   ⋆ This question says that we have to find out the final velocity when a particle covers a distance of 2 kilometres and it is starts from rest and then it is moving with a uniform acceleration of [tex]{\sf{10 \: ms^{-2}}}[/tex] Let’s solve this question!

   [tex]{\bigstar \:{\pmb{\sf{\underline{Provided \: that…}}}}}[/tex]

   [tex]\sf According \: to \: statement \begin{cases} & \sf{Acceleration \: = \bf{10 \: ms^{-2}}} \\ \\ & \sf{Initial \: velocity \: = \bf{0 \: ms^{-1}}} \\ \\ & \sf{Distance \: = \bf{2 \: kilometres}} \\ \\ & \sf{Final \: velocity \: = \bf{?}} \end{cases}\\ \\[/tex]

   Don’t be confused! Initial velocity came as zero because the body that is particle here is at rest.

   [tex]{\bigstar \:{\pmb{\sf{\underline{Using \: concept…}}}}}[/tex]

   ⋆ Third equation of motion.

   ⋆ Formula to convert kilometres into metres.

   [tex]{\bigstar \:{\pmb{\sf{\underline{Using \: formula…}}}}}[/tex]

   ⋆ Third equation of motion is given by

   • [tex]{\small{\underline{\boxed{\sf{2as \: = v^2 – u^2}}}}}[/tex]

   (Where, a denotes acceleration , s denotes displacement or distance or height , v denotes final velocity , ² means square and u denotes initial velocity)

   ⋆ Kilometres to metres,

   • [tex]{\small{\underline{\boxed{\sf{1 \: km \: = 1000 \: metres}}}}}[/tex]

   [tex]{\bigstar \:{\pmb{\sf{\underline{Full \; Solution…}}}}}[/tex]

   ~ Firstly let us convert kilometres into metres.

   [tex]:\implies \sf 1 \: km \: = 1000 \: metres \\ \\ :\implies \sf 2 \times 1000 \\ \\ :\implies \sf 2000 \: metres[/tex]

   ~ Now let’s find final velocity.

   [tex]:\implies \sf 2as \: = v^2 – u^2 \\ \\ :\implies \sf 2(10)(2000) = v^2 – 0^2 \\ \\ :\implies \sf 2(20000) = v^2 – 0^2 \\ \\ :\implies \sf 2(20000) = v^2 \\ \\ :\implies \sf 40000 = v^2 \\ \\ :\implies \sf \sqrt{40000} = v \\ \\ :\implies \sf 200 = v \\ \\ :\implies \sf v = 200 \: ms^{-1} \\ \\ :\implies \sf Final \: velocity \: = 200 \: ms^{-1}[/tex]

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