Question

A train moves from rest to a speed of 25 m/s in 30 seconds. What is the magnitude of its acceleration?

Answer 1

Given:-

• Initial velocity ,u = 0m/s
• Final velocity ,v = 25m/s
• Time taken ,t = 30

To Find:-

• Magnitude of Acceleration ,a

Solution:-

we have to calculate the magnitude of acceleration.

As we know that acceleration is defined as the rate of change in velocity .

• a = v-u/t

where

• v is the final velocity
• a is the acceleration
• u is the initial velocity
• t is the time taken

Substitute the value we get

$:\implies$ a = 25-0/30

$:\implies$ a = 25/30

$:\implies$ a = 0.833 m/s²

• Hence, the acceleration of the train is 0.833 m/s².

Answer 2

Given that , A train moves from rest to a speed of 25 m/s in 30 seconds .

Exigency To Find : The magnitude of Acceleration of train .

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀⠀Given that ,

• The initial velocity ( u ) of train is 0 m/s [ as , train starts from rest ] .
• The final velocity ( v ) of train is 25 m/s .
• Total Time taken ( t ) is 30 seconds .

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Finding Magnitude of Acceleration of Train :

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

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

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

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

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

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

$\qquad \dashrightarrow \sf \: Acceleration\: (\:a\:)\: =\: \dfrac{\:\:25\:\: - \:\:0\:\:}{30}\:\:$

$\qquad \dashrightarrow \sf \: Acceleration\: (\:a\:)\: =\: \dfrac{\:\:25\:\:\:}{30}\:\:$

$\qquad \dashrightarrow \sf \: Acceleration\: (\:a\:)\: =\: \cancel {\dfrac{\:\:25\:\:\:}{30}}\:\:$

$\qquad \dashrightarrow \sf \: Acceleration\: (\:a\:)\: =\: 0.833 \:\:\:\:$

$\qquad \therefore \:\:\pmb{\underline{\purple{\frak{ \:Acceleration\: (\:a\:)\: = \:0.833 \:m\:/s^2 \: }}} }\bigstar$

• Here, a denotes Magnitude of Acceleration which is 0.833 m/s²

$\qquad \therefore \:\underline { \sf Hence , \:\: The \: \:Magnitude \:\: of \:\: the \:\:Acceleration \:\: is \:\:\bf \:0.833 \:m/s^2 \:\:.}$