A body has initial velocity of 3 m/s and has an
acceleration of 2 m/s². The distance travelled
by it in 5 s and its velo

2 thoughts on “A body has initial velocity of 3 m/s and has an<br />acceleration of 2 m/s². The distance travelled<br />by it in 5 s and its velo”

1. [tex]\large{\mathbb{\colorbox{nav} {\boxed{\boxed{\colorbox{white} {-:Answer:-}}}}}}[/tex]

   [tex]\large{ \pmb{ \underline{ \underline{\frak{ \color{navy}{Given::}}}}}}[/tex]

   [tex]\pink{➠}{ \sf{Initial \: velocity(u) \: of \: body={ \rm 3}m {s}^{ – \rm 1} }}[/tex]

   [tex]\pink{➠}{ \sf{Acceleration(a) \: of \: body={ \rm 2}m {s}^{ -{ \rm 2}} }}[/tex]

   [tex]\pink{➠}{ \sf{Time(t) \: taken \: to \: change \: the \: velocity\: of \: body={ \rm 5}s }}[/tex]

   [tex]\large{ \pmb{ \underline{ \underline{\frak{ \color{nav}{To \: find::}}}}}}[/tex]

   [tex]\pink{➠}{ \sf{Distance(s) \: travelled \: by \: body \: in \: {\rm 5}s. }}[/tex]

   [tex]\pink{➠}{ \sf{Final \: velocity(v) \: of \: body. }}[/tex]

   [tex]\large{ \pmb{ \underline{ \underline{\frak{ \color{violet}{Formula \: required::}}}}}}[/tex]

   [tex]\pink{➠}{ \sf{s = ut + \frac{1}{2} a {t}^{2} \: \: … \{(i) \} \{{By \: 2nd \: equation \: of \: motion} \}}}[/tex]

   [tex]\pink{➠}{ \sf{v= u + at \: \: … \{(ii)\} \{{By \: 1st \: equation \: of \: motion} \}}}[/tex]

   [tex] \pmb{ \bf{Focus \: point;}}[/tex]

   [tex]\pink{➠}{ \bf{ We \: use \: to \: represent,}}[/tex]

   [tex]{: : \implies \sf{s=Distance \: covered \: by \: body}}[/tex]

   [tex]{: : \implies \sf{u=Initial \: velocity \: of\: body}}[/tex]

   [tex]{: : \implies \sf{v=Final \: velocity \: of\: body}}[/tex]

   [tex]{: : \implies \sf{a=Acceleration\: of\: body}}[/tex]

   [tex]\large{ \pmb{ \underline{ \underline{\frak{ \color{purple}{According \: to \: Question::}}}}}}[/tex]

   [tex] \pmb{ \bf{Let’s \: start \: directly \: with \: the \: help \: of \: formulas!!! }}[/tex]

   [tex] \bf{Let’s \: find \: the \: distance \: covered \: by \: body;}[/tex]

   [tex]\pink{➠}{ \sf{s = ut + \frac{1}{2} a {t}^{2} \: \: … \{from \: equation(i) \}}}[/tex]

   [tex] \bf{Substituting \: the \: values \: in \: equation(i),}[/tex]

   [tex]: : \implies{ \sf{s ={ \rm \: 3 \times 5 + \frac{1}{2} \times 2 \times {(5)}^{2} }}}[/tex]

   [tex]: : \implies{ \sf{s ={ \rm \: 3 \times 5 + \frac{1}{ \cancel 2} \times \cancel 2 \times {(5)}^{2} }}}[/tex]

   [tex]: : \implies{ \sf{s ={ \rm \: 3 \times 5 + 1\times 25 }}}[/tex]

   [tex]: : \implies{ \sf{s ={ \rm \: 15 + 25 }}}[/tex]

   [tex]: : \implies{ \sf{s = { \rm \: 40}m }}[/tex]

   [tex] \bf{Hence, }[/tex]

   [tex]\dag \underline{\boxed{ \red{ \sf{{Distance(s) \: travelled \: by \: body \: in \: {\rm 5}s = {\rm40 }m}}}}}[/tex]

   [tex] \bf{Again, to \: find \: the \: final \: velocity(v) \: of \: body;}[/tex]

   [tex]\pink{➠}{ \sf{v = u + at \: \: … \{from \: equation(ii) \}}}[/tex]

   [tex] \bf{Substituting \: the \: values \: in \: equation(ii),}[/tex]

   [tex]: : \implies{ \sf{v={ \rm 3 + 2 \times 5 }}}[/tex]

   [tex]: : \implies{ \sf{v={ \rm 3 + 10}}}[/tex]

   [tex]: : \implies{ \sf{v={ \rm 13}m {s}^{ – 1} }}[/tex]

   [tex] \bf{Hence, }[/tex]

   [tex]\dag \underline{\boxed{ \red{ \sf{{Final \: velocity (v) \: of \: body = {\rm \: 13 }m {s}^{ – 1} }}}}}[/tex]

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2. Yᴏᴜʀ Qᴜᴇsᴛɪᴏɴ ;

   • A body has initial velocity of 3 m/s and has an
   • acceleration of 2 m/s². The distance travelled
   • by it in 5 s and its velocity is.

   Gɪᴠᴇɴ :

   • Initial velocity (u) ᴏf the body ➠ 3 m/s.
   • Acceleration (a) ᴏf the body ➠ 2 m/s².
   • Time (t) ➠ 5s.

   To Fɪɴᴅ :

   • Distance travelled by the body.
   • Vellocity of the body.

   Fᴏʀᴍᴜʟᴀ ᴜsᴇᴅ :

   [tex] \\ ✰ \: \: {\color{purple}{\underline{ \boxed{ \frak{ \pmb {\pmb{S \: = \: ut \: + \: \frac{1}{2} \: a \: t {}^{2} }}}}}}} \: \: ✰ \: \: \: \:[/tex][ Used for finding the distance covered (s) ]

   [tex]\\ ✰\:\:{\underline{\boxed{ \pmb{\frak{{ \color{purple}v\:=\:u\:+\:a\:t\:}}}}}} \: \: ✰ \: \: \: \: [/tex][ Used for finding the velocity ]

   Rᴇǫᴜɪʀᴇᴅ Sᴏʟᴜᴛɪᴏɴ ;

   [tex] \\ {\sf{ \pmb{ \underline{{ \huge{ \color{purple}\star} }\: Here \: : }}}} \begin{cases}✪ \: { \underline{ \pmb{ Distance \: covered \: = \bf \: s.}}} \\ ✪ \: { \underline{ \pmb{{Initial \: velocity \: = \bf \: u.} }}} \\ ✪ \:{ \underline{ \pmb{{Time\: = \bf \: t.}}}} \\ ✪ \: {{ \underline{ \pmb{{Acceleration\: = \bf \: a.}}}}}\end{cases} \\ \\ [/tex]

   [tex]❍ \: \: \pmb{\sf{ \: \underline {Calculating \: the \: distance \: covered \: (s) \: : }}} \\ \\ [/tex]

   [tex]༒ \: \: \frak{ \pmb{ \: \underline {Substituting \: the \: values \: according \: to \: the \: formula \: :} }} \\ \\ [/tex]

   [tex] \\ ➲ \: \tt{S\:=\:3\times{5}\:+\:\dfrac{1}{2}\times{2}\times{5^2}\:} \\\\\ ➲ \: \tt{S\:=\:15\:+\:25\:} \\\\\ ✰ \: \:\underline{ \boxed{\frak{\color{purple}{➠\:S\:=\:40\:m}}}} \: \: ✰ \\ \\ [/tex]

   [tex]{ \therefore \: \pmb{ \underline{Hence \: \: the \: \: distance \: \: covered \: \: by \: \: the \: \: body \: \: is \: \: \: \bf{40 \: m.}}}}[/tex]

   Tʜᴇɴ,

   [tex]❍ \: \: \pmb{\sf{ \: \underline {Calculating \: the \: velocity \: : }}} \\ \\ [/tex]

   [tex]༒ \: \: \frak{ \pmb{ \: \underline {Substituting \: the \: values \: according \: to \: the \: formula \: :} }} \\ \\ [/tex]

   [tex]➣ \: \: \sf{v\:=\:3\:+\:2\times{5}\:} \\\\\ ➣ \: \: \sf{v\:=\:3\:+\:10\:} \\\\\ ✰\: \:{ \underline{ \boxed{\frak{\purple{➠ \: v\:=\:13\:m/s}}}}} \: \: ✰ \\ [/tex]

   [tex]{ \therefore \: \pmb{ \underline{Hence \: \: the \: \: velocity \: \: is \: \: \: \bf{13m/s \: .}}}} \\ \\ [/tex]

   ✰ Hᴏᴘᴇ ɪᴛ ʜᴇʟᴘs ᴜ ✰

   [tex]\\\\ \large{{ \fcolorbox{lime}{black}{{ \bf{ \color{blue}H}{\red{A}}{ \color{darkviolet}P}{ \orange{P}}{ \purple{Y }} \: {\pink{H}}{ \color{cyan}O}{ \color{purple}L}{ \color{pink}I}}}}}[/tex]

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