Question

A car starts from rest and attains a speed of 72 km/h in 5 seconds. Find the acceleration of the car.​

Answer 1

✬ Acceleration = 5 m/s² ✬

Explanation:

Given:

• A car stars from rest.
• Final speed of car is 72 km/h.
• Time taken to attain final speed is 5 seconds.

To Find:

• What is the acceleration of the car ?

Formula to be used:

• v = u + at

Solution: Let the acceleration of the car be a m/s².

First of all lets change km/h to m/s by multiplying with 5/18.

➟ v = 72 × 5/18

➟ v = 4 × 5 = 20 m/s

Here we have

• u = 0 m/s

• v = 20 m/s

• t = 5 s

• a = a m/s²

Putting all the values on above formula

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

$\implies{\rm }$ 20 = 0 + a × 5

$\implies{\rm }$ 20 = 5a

$\implies{\rm }$ 20/5 = a

$\implies{\rm }$ 4 m/s² = a

Hence, the acceleration of the car is 4 m/s².

Answer 2

Given : A car starts from rest and attains a speed of 72 km/h in 5 seconds .

Exigency To Find : The Acceleration of car ?

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀⠀Given that ,

⠀⠀⠀⠀⠀⠀⠀▪︎⠀The initial velocity ( u ) of car is 0 m/s [ as , car starts from rest ]

⠀⠀⠀⠀⠀⠀⠀▪︎⠀The total time taken is 5 seconds

⠀⠀⠀⠀⠀⠀⠀▪︎⠀The Final velocity ( v ) of car is 72 km/h

⠀⠀⠀Converting Final Velocity from km / h to m / s :

$\qquad:\implies \sf Final \:Velocity \: = \: 72 \:\:km/h$

As , We know that ,

• For changing the unit from km / h to m / s we multiply it by 5/18 .

$\qquad:\implies \sf Final \:Velocity \: = \: 72 \:\:\times \:\:\dfrac{5}{18}$

$\qquad:\implies \sf Final \:Velocity \: = \: \cancel {72} \:\:\times \:\:\dfrac{5}{\cancel{18}}$

$\qquad:\implies \sf Final \:Velocity \: = \: 4 \:\:\times \:\:5$

$\qquad:\implies \sf Final \:Velocity \: = \: 20 \:$

$\qquad \therefore \pmb{\underline{\purple{\frak{\:Final \:Velocity\:(\:or\: v\:) \: = \: 20 \: m/s }} }}\:\:\bigstar$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Finding  Acceleration  of car :

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

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

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

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

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

$\qquad \dashrightarrow \sf Acceleration\:(a)\:=\:\dfrac{ \:\: 20\:\:- \:\:0\:\:}{5}\:\: \\\\\qquad \dashrightarrow \sf Acceleration\:(a)\:=\:\dfrac{ \:\: 20\:\:\:\:}{5}\:\: \\\\\qquad \dashrightarrow \sf Acceleration\:(a)\:=\:\cancel {\dfrac{ \:\: 20\:\:\:\:}{5}}\:\: \\\\\qquad \dashrightarrow \sf Acceleration\:(a)\:=\:4 \:\: \\\\\qquad \therefore \pmb{\underline{\purple{\frak{\:\: Acceleration\:(a)\:=\:4 \:\: m/s^2 }} }}\:\:\bigstar$

$\qquad \therefore \underline {\:\sf \: Hence, \: The \: Acceleration \:of \:car \: is \: \bf 4 \:\: m/s^2\:}$