Question

Starting from rest rohan attains a velocity of 12m\s in 30 sec than he applies brakes the velocity comes down by 8m\s in next 5 sec calculate accelaration in both cases

Answer 1

${\bigstar \:{\pmb{\sf{\underline{Understanding \: the \: question...}}}}}$

⋆ This question says that we have to find out the acceleration in both cases if the condition is mentioned as Rohan attains a velocity of 12 m/s in 30 seconds when starting from the rest. Afterthat covering..., he applies brake then the velocity comes down by 8 m/s in next 5 seconds.

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

⋆ Formula to calculate acceleration.

${\small{\underline{\boxed{\sf{\dfrac{Change \: in \: velocity}{Time}}}}}}$

• It can be also written as

${\small{\underline{\boxed{\sf{a \: = \dfrac{v - u}{t}}}}}}$

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⠀⠀⠀⠀${\large{\bigstar \:{\pmb{\sf{\underline{Case \: 1^{st}}}}}}}$

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

$\sf According \: to \: statement \begin{cases} & \sf{Initial \: velocity \: = \bf{0 \: m/s}} \\ \\ & \sf{Time \: = \bf{30 \: seconds}} \\ \\ & \sf{Final \: velocity \: = \bf{12 \: m/s}} \\ \\ & \sf{Acceleration \: = \bf{?}} \end{cases}$

Don't be confused! Initial velocity came as zero because the object starts from rest.

${\underline{\tt{Now \: let's \: calculate \: acceleration}}}$

$:\implies \sf Acceleration \: = \dfrac{Change \: in \: velocity}{Time} \\ \\ :\implies \sf a \: = \dfrac{v - u}{t} \\ \\ :\implies \sf a \: = \dfrac{12-0}{30} \\ \\ :\implies \sf a \: = \dfrac{12}{30} \\ \\ :\implies \sf a \: = \dfrac{6}{15} \\ \\ :\implies \sf a \: = \dfrac{2}{5} \\ \\ :\implies \sf a \: = 0.4 \: m/s^2 \\ \\ {\pmb{\sf{:\implies Acceleration \: = 0.4 \: m/s^2}}}$

Henceforth, 0.4 m/s² is the acceleration in the case first!

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⠀⠀⠀⠀${\large{\bigstar \:{\pmb{\sf{\underline{Case \: 2^{nd}}}}}}}$

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

$\sf According \: to \: statement \begin{cases} & \sf{Initial \: velocity \: = \bf{12 \: m/s}} \\ \\ & \sf{Time \: = \bf{5 \: seconds}} \\ \\ & \sf{Final \: velocity \: = \bf{8 \: m/s}} \\ \\ & \sf{Acceleration \: = \bf{?}} \end{cases}$

${\underline{\tt{Now \: let's \: calculate \: acceleration}}}$

$:\implies \sf Acceleration \: = \dfrac{Change \: in \: velocity}{Time} \\ \\ :\implies \sf a \: = \dfrac{v - u}{t} \\ \\ :\implies \sf a \: = \dfrac{8-12}{5} \\ \\ :\implies \sf a \: = \dfrac{-4}{5} \\ \\ :\implies \sf a \: = -0.8 \: m/s^2 \\ \\ {\pmb{\sf{:\implies Acceleration \: = -0.8 \: m/s^2}}}$

Henceforth, -0.8 m/s² is the acceleration in the case second!