Question

A roller coaster is traveling at 13 m/s when it approaches a hill that is 400 m long. Heading down the hill, it accelerates at 4.0 m/s^2. Find the final velocity of the roller coaster ?​

Answer 1

`{\mathfrak{\underline{\purple{\:\:\: Given:-\:\:\:}}}} \\ \\`

`\:\:\:\:\bullet\:\:\:\sf{Initial \ velocity \ (u) = 13 \ m/s }`

`\:\:\:\:\bullet\:\:\:\sf{Distance \ (s) = 400 \ m }`

`\:\:\:\:\bullet\:\:\:\sf{ Acceleration = 4 \ m/s^2}`

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`{\mathfrak{\underline{\purple{\:\:\:To \:Find:-\:\:\:}}}} \\ \\`

`\:\:\:\:\bullet\:\:\:\sf{The \:Final \:velocity \:of \:the\: body }`

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`{\mathfrak{\underline{\purple{\:\:\: Calculation:-\:\:\:}}}} \\ \\`

☯ Using 3rd equation of motion

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`\dashrightarrow\:\: \sf{ {v}^(2) = {u}^(2) +2as }`

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`\dashrightarrow\:\: \sf{ {v}^(2) = {13}^(2) + 2 * 4 * 400 }`

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`\dashrightarrow\:\: \sf{{v}^(2) = 169 + 3200 }`

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`\dashrightarrow\:\: \sf{ {v}^(2) = 3369 }`

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`\dashrightarrow\:\: \sf{ v = √(3369) }`

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`\dashrightarrow\:\: \underline{\boxed{\sf{ v = 58.04 \: m/s }}}`

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`{\mathfrak{\underline{\purple{\:\:\:Additional \:Information:-\:\:\:}}}} \\ \\`

☢ Equations Of Motion

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`\boxed{</p><p></p><p>\begin{minipage}{3 cm}$\\</p><p></p><p>\sf{\:\:\star\:\:v = u +at} \\ \\</p><p></p><p>\sf{\:\:\star\:\:s = ut + (1)/(2)\:at^(2) }\\ \\</p><p></p><p>\sf{\:\:\star\:\:v^(2) = u^(2) + 2as}\\ \\</p><p>\sf{\:\:\star\:\:s = (1)/(2) (u + v)t}\\$</p><p></p><p>\end{minipage}</p><p></p><p>}`

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`\sf{Where,}`

`\:\:\:\:\bullet\:\:\:\textsf{v = Final velocity}`

`\:\:\:\:\bullet\:\:\:\textsf{u = Initial velocity}`

`\:\:\:\:\bullet\:\:\:\textsf{a = Acceleration}`

`\:\:\:\:\bullet\:\:\:\textsf{s = Distance}`

`\:\:\:\:\bullet\:\:\:\textsf{t = Time taken}`