Question

how much force is required to change the velocity of an object of mass 20 kg from 10m/s to 20 m/s in 4s​

Answer 1

$\sf\small\underline\green{Given:-}$

$\sf{\implies mass\:of\: object=20\:kg}$

$\sf{\implies Final\: velocity=20\:m/s}$

$\sf{\implies Initial\: velocity=10\:m/s}$

$\sf{\implies Time\: taken=4\:s}$

$\sf\small\underline\green{To\: Find:-}$

$\sf{\implies Force\: required=?}$

$\sf\small\underline\green{Solution:-}$

To solve this problem at first we have to find out acceleration by applying the formula of first equation of motion. The calculate force required to change the velocity of an object of mass 20kg.

$\sf\small\underline\green{Formula\:Used:-}$

$\sf{\implies v=u+at}$

$\sf{\implies v=Final\: velocity,\:u=Initial\: velocity}$

$\sf{\implies a=acceleration,\:t=time}$

$\rm{\implies v=u+at}$

$\rm{\implies 20=10+a*4}$

$\rm{\implies 20=10+4a}$

$\rm{\implies 20-10=a*4}$

$\rm{\implies 4a=10}$

$\rm{\implies a=2.5\:m/s^2}$

• Now calculate force required :-

$\sf{\implies Force=mass\times\: acceleration}$

$\rm{\implies Force=20\times\:2.5}$

$\rm{\implies Force=50\:N}$

$\sf\large{Hence,}$

$\bf{\implies Force\: required=50\:N}$

Answer 2

Given that , The change in velocity of an object of mass 20 kg from 10m/s to 20 m/s in 4 seconds .

Exigency To Find , The amount of Force Required to change velocity.

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀⠀⠀⠀Given that ,

• The initial velocity ( u ) of an object is 10 m/s ,
• The Final Velocity ( v ) of an object is 20 m/s &
• Total Time taken ( t ) is 4 second.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀¤ Finding Acceleration of an object :

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

$\qquad \dag\:\:\bigg\lgroup \pmb{\bf{ \:\:\:Acceleration\:(\:or\:a\:)\: :\:\dfrac{\:\:v \:-\:u\:\:}{t}\:\:\: }}\bigg\rgroup$

⠀⠀⠀Here , v is the final velocity , u is the Initial velocity , t is the total time taken and a is the Acceleration.

$\qquad \dashrightarrow \sf \:\:\:Acceleration\:(\:or\:a\:)\: =\:\dfrac{\:\:v \:-\:u\:\:}{t}\:\:\: \:\:$

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad \dashrightarrow \sf \:\:\:Acceleration\:(\:or\:a\:)\: =\:\dfrac{\:\:v \:-\:u\:\:}{t}\:\:\: \:\:$

$\qquad \dashrightarrow \sf \:\:\:Acceleration\:(\:or\:a\:)\: =\:\dfrac{\:\:20 \:-\:10\:\:}{4}\:\:\: \:\:$

$\qquad \dashrightarrow \sf \:\:\:Acceleration\:(\:or\:a\:)\: =\:\dfrac{\:10\:\:}{4}\:\:\: \:\:$

$\qquad \dashrightarrow \sf \:\:\:Acceleration\:(\:or\:a\:)\: =\:\cancel {\dfrac{\:10\:\:}{4}}\:\:\: \:\:$

$\qquad \dashrightarrow \sf \:\:\:Acceleration\:(\:or\:a\:)\: =\:2.5 \:\:\:\: \:\:$

$\qquad \therefore \pmb{\underline{\purple{\frak{\:\: \:\:\:Acceleration\:(\:or\:a\:)\: =\:2.5 \:\:m/s^2 \:\: }}} }\:\:\bigstar$

$\qquad \therefore \:\:\underline {\sf \:\: Acceleration \:of \:an \:object \:is \: \bf 2.5 \: m/s^2 \: }$

⠀⠀⠀⠀⠀⠀⠀⠀Now ,

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀¤ Finding Amount of Force Required :

$\dag\:\:\pmb{ As,\:We\:know\:that\::}\\\\\qquad\maltese\bf \:Formula\:for \:Force\::$

$\qquad \dag\:\:\bigg\lgroup \pmb{\bf{ \:\:\:Force\:(\:or\:F\:)\: :\:ma\:\:\: }}\bigg\rgroup$

⠀⠀⠀⠀⠀⠀⠀⠀Here , m is the mass , a is the Acceleration & F is the Force .

$\qquad \dashrightarrow \sf \:Force\:(\:or\:F\:)\:=\:ma\:\:\:$

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}\\\\ \dashrightarrow \sf \:Force\:(\:or\:F\:)\: =\:ma\:\:\: \\\\ \dashrightarrow \sf \:Force\:(\:or\:F\:)\: =\:20 \:\times \: 2.5\:\:\: \\\\ \dashrightarrow \sf \:Force\:(\:or\:F\:)\: =\:50\:\:\: \\\\ \therefore \pmb{\underline{\purple{\frak{\:\:\:Force\:(\:or\:F\:)\: =\:50\:\:N\: }}} }\:\:\bigstar$

$\therefore \:\:\underline {\sf \:\: Hence, \: Amount \:of \: Force \:required \:to\:change \:the \:velocity \:is \: \bf 50 \: N \: }$