A fish swimming at a constant speed of 0.5 m/s suddenly notices a shark appear behind it. 5 seconds later, the fish swimming in t

By Eva

A fish swimming at a constant speed of 0.5 m/s suddenly notices a shark appear behind it. 5 seconds later, the fish swimming in the same direction at a speed of 2.5 m/s. Calculate the fish’s acceleration. *

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  1. Given : A fish swimming at a constant speed of 0.5 m/s [ as , Initial Velocity ( u ) ] , After noticing the shark fish’s speed is 2.5 m/s [ as , Final Velocity ( v ) ] & Time taken is 5 seconds [ as , Time ( t ) ]

    Exigency To Find : The Acceleration of fish ?

    ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

    ⠀⠀⠀⠀Given that ,

    ⠀⠀⠀⠀⠀⠀⠀⠀▪︎⠀⠀The initial velocity ( u ) of fish is 0.5 m/s .

    ⠀⠀⠀⠀⠀⠀⠀⠀▪︎⠀⠀The final velocity ( v ) of fish is 2.5 m/s

    ⠀⠀⠀⠀⠀⠀⠀⠀▪︎⠀⠀Total Time taken ( t ) is 5 seconds

    ⠀⠀⠀⠀⠀⠀⠀Finding Acceleration of fish :

    [tex]\dag\:\:\pmb{ As,\:We\:know\:that\::}\\\\ \qquad \bigstar \:\: \bf Acceleration \: : \: \sf The \: rate \:of \: of \: change \:of\: velocity\:is \:known \: as \: Acceleration \:. \:\\\\ \qquad\maltese\:\:\bf Formula \:for \: Acceleration\:: \\[/tex]

    [tex]\qquad \dag\:\:\bigg\lgroup \pmb{\bf{\;\: Acceleration\:(a)\:=\:\dfrac{ \:\: v \:\:- \:\:u\:\:}{t}\:\: }}\bigg\rgroup \\\\[/tex]

    ⠀⠀⠀⠀Here , u is the Initial velocity, v is the final velocity & t is the time taken .

    [tex]\qquad \dashrightarrow \sf Acceleration\:(a)\:=\:\dfrac{ \:\: v \:\:- \:\:u\:\:}{t}\qquad \:\\\\[/tex]

    ⠀⠀⠀⠀⠀⠀[tex]\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}\\[/tex]

    [tex]\qquad \dashrightarrow \sf Acceleration\:(a)\:=\:\dfrac{ \:\: v \:\:- \:\:u\:\:}{t}\qquad \:\\\\[/tex]

    [tex]\qquad \dashrightarrow \sf Acceleration\:(a)\:=\:\dfrac{ \:\: 2.5 \:\:- \:\:0.5\:\:}{5}\qquad \:\\\\[/tex]

    [tex]\qquad \dashrightarrow \sf Acceleration\:(a)\:=\:\dfrac{ \:\: 2\:\:}{5}\qquad \:\\\\[/tex]

    [tex]\qquad \dashrightarrow \sf Acceleration\:(a)\:=\:\cancel {\dfrac{ \:\: 2\:\:}{5}}\qquad \:\\\\[/tex]

    [tex]\qquad \dashrightarrow \sf Acceleration\:(a)\:=\:0.4 \:\qquad \:\\\\[/tex]

    [tex]\qquad \therefore \pmb{\underline{\purple{\frak{ \:Acceleration\:(a)\:=\:0.4 \:m/s^2 }}} }\:\:\bigstar \\[/tex]

    [tex]\therefore \:\underline { \sf Hence , \:\: The \:Acceleration \:of\:fish\:is \: \bf 0.4 \: m/s^2 \:}.\\\\[/tex]

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  2. Answer:

    The acceleration of the fish is 0.4 m/s².

    Explanation:

    Fish was swimming at the speed of = 0.5 m/s

    Time = 5 seconds

    Fish’s speed after noticing the shark = 2.5 m/s

    Acceleration of the fish = ??

    _____________________________

    [tex]\bigstar \: {\boxed{\sf{ Acceleration = \dfrac{v – u}{t}}}}[/tex]

    • v = 2.5 m/s
    • u = 0.5 m/s
    • t = 5 seconds

    [tex]\sf{\longrightarrow} \: \dfrac{2.5 – 0.5}{5} [/tex]

    [tex]\sf{\longrightarrow} \: \dfrac{2}{5} [/tex]

    [tex]\sf{\longrightarrow} \: 0.4 \: {ms}^{ – 2} [/tex]

    Acceleration of the fish = 0.4 m/s²

    Therefore, the acceleration of the fish is 0.4 m/s².

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