Question

The velocity of a body changes from 50 m/s - 80 m/s by Time of 10 s . What is distance covered by body if acceleration is 2.01 m/s2.​

Answer 1

$\large \sf {\underbrace{\underline{Elucidation:-}}}$

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$\sf \rm \red {\underline{Provided\: that:}}$

$\mapsto \tt {Initial\: Velocity\: (u)=50m/s}$

$\mapsto \tt {Final\: Velocity\: (v)=80m/s}$

$\mapsto \tt {Time\: interval\: (t)=10s}$

$\mapsto \tt {Acceleration\: (a)=2.01m/s^{2}}$

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$\sf \rm \blue {\underline{To\: be\: determined:}}$

$\mapsto \tt {Distance\: covered\: by}$ $\tt {the\: body\: (s)=?}$

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$\sf \rm \orange {\underline{Using\: 3^{rd}\: equation\: of\: motion:}}$

$\colon \implies \tt {\boxed{v^{2}=u^{2}+2as}}$

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★Supplanting the given values,

$\colon \mapsto \tt {(80m/s)^{2}=(50m/s)^{2}+2\times 2.01m/s^{2} \times s}$

$\colon \mapsto \tt {6400=2500+4.02\times s}$

$\colon \mapsto \tt {6400-2500=4.02\times s}$

$\colon \mapsto \tt {3900=4.02\times s}$

$\large \colon \mapsto \tt {s=\frac{3900}{4.02}}$

$\large \colon \mapsto \tt {s=\frac{3900\times 100}{402}}$

$\colon \mapsto \tt {s≈970.14}$

$\colon \implies \tt \green {\fbox{s=970m(Apx)}}$

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$\sf \rm \purple {\underline{Thusforth,}}$

★The distance covered by the body is approximately "970m"

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Answer 2

$\large \frak{Given} \begin{cases} \quad \sf initial \: velocity(u) = 50m {s}^{ - 1} \\ \quad \sf final \: velocity(v) = 80 m{s}^{ - 1} \\ \quad \sf acceleration(a) =2.01m {s}^{ - 2} \\ \quad \sf time \: taken(t) = 10s \end{cases}$

$\maltese\: \large\underbrace{\purple{\frak{Solution:-}}}$

$\dag\underline{\sf{By \:using\: 3rd\: Kinematical \:equation :- }}$

$\\ \leadsto \large\underline{ \boxed{ \pink{\sf {v}^{2} - {u}^{2} = 2as}}} \bigstar$

Where, v, u, a and s represents Final velocity, Initial velocity, Acceleration and Distance.

$\dag\underline{\sf{Substitute \:the \:values \:into \: it!! }}$

$\\ \quad \rightarrow\sf {(80)}^{2} - {(50)}^{2} = 2 \times 2.01 \times S$

$\\ \quad \rightarrow \sf 6400 - 2500 = 4.02 \times S$

$\\ \quad \rightarrow \sf \dfrac{3900}{4.02} = S$

$\\ \quad \rightarrow \sf S = 970.14 \: m$

$\\ \quad \rightarrow \boxed{ \boxed{ \orange{\sf S \approx 970 \: m}}} \bigstar$

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