Question

$a \: body \: moving \: with \: a \: constant \: acceleration \: and \: travels \: 270 \: m \: in \: 3 \:s. \: find \: the \: velocity \: of \: the \: body \: at \: 10 \: s \: after \: the \: start.$
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Answer 1

${\large{\pmb{\sf{\underline{RequirEd \: Solution...}}}}}$

⋆ Correct question: A body moving with a constant acceleration and travels 270 m in 3 s. Find the velocity of the body at 10 s after the start.

⋆ Understanding the question: This question says that we have to find out the velocity of the body at 10 seconds after the start if a body is moving with a constant acceleration and travels 270 metres in 3 seconds.

$\sf \star \: \: According \: to \: statement \begin{cases} & \sf{Initial \: velocity \: = \bf{0 \: m/s}} \\ \\ & \sf{Final \: velocity \: = \bf{?}} \\ \\ & \sf{Actual \: time \: = \bf{3 \: seconds}} \end{cases}$

Don't be confused! Initial velocity came as zero because a body moving with a constant acceleration...

⋆ Concepts to imply:

• First equation of motion.

${\small{\boxed{\underline{\sf{v \: = u \: + at}}}}}$

• Second equation of motion.

${\small{\boxed{\underline{\sf{s \: = ut \: + \dfrac{1}{2} \times at^2}}}}}$

(Where, v denotes final velocity , u denotes initial velocity , a denotes acceleration , t denotes time , s denotes displacement or distance)

⋆ Let's solve this question!

~ Firstly let us use second equation of motion, for finding the acceleration.

${\sf{\dashrightarrow s \: = ut \: + \dfrac{1}{2} \times at^2}}$

${\sf{\dashrightarrow 270 = 0(3) + \dfrac{1}{2} \times a(3)^{2}}}$

${\sf{\dashrightarrow 270 = 0 + \dfrac{1}{2} \times a(9)}}$

${\sf{\dashrightarrow 270 = \dfrac{1}{2} \times a(9)}}$

${\sf{\dashrightarrow 270 = \dfrac{1}{2} \times 9a}}$

${\sf{\dashrightarrow 270 \times 2 = 1 \times 9a}}$

${\sf{\dashrightarrow 540 = 1 \times 9a}}$

${\sf{\dashrightarrow 540 = 9a}}$

${\sf{\dashrightarrow \dfrac{540}{9} = a}}$

${\sf{\dashrightarrow 60 = a}}$

${\sf{\dashrightarrow a = \: 60 \: m/s^2}}$

${\sf{\dashrightarrow Acceleration = \: 60 \: m/s^2}}$

~ Now let us use first equation of motion to find the final velocity! But now we have to put 10 seconds as time not 3 seconds beacuse the question says that find out the velocity of the body at 10 seconds...

${\sf{\dashrightarrow v \: = u \: + at}}$

${\sf{\dashrightarrow v \: = 0 + 60(10)}}$

${\sf{\dashrightarrow v \: = 0 + 600}}$

${\sf{\dashrightarrow v \: = 600 \: m/s}}$

${\sf{\dashrightarrow Final \: velocity \: = 600 \: m/s}}$