Question

1. A bus starting from rest moves
with a uniform acceleration of
0.1 m s2 for 2 minutes. Find (a)
the speed acquired, (b) the
distance travelled.​

Answer 1

Given :

Initial velocity ,u= 0 m/s

Accelaration , a= 0.1 m/s²

Time , t = 2 min = 120 sec

To Find :

• The speed acquired
• The distance travelled by the bus

${\purple{\boxed{\large{\bold{Formula's}}}}}$

Kinematic equations for uniformly accelerated motion.

$\bf\:v=u+at$

$\bf\:S=ut+\frac{1}{2}at{}^{2}$

$\bf\:v{}^{2}=u{}^{2}+2aS$

and $\bf\:s_{nth}=u+\frac{a}{2}(2n-1)$

${\underline{\sf{Answer}}}$

1) We have to the find the final velocity of the bus

By First Equation of motion

$\rm\:v=u+at$

Put the given values

$\sf\implies\:v=0+0.1\times120$

$\sf\implies\:v=12ms^{-1}$

Therefore, the final velocity of the bus is 12m/s

2) We have to find the distance travelled by the bus

By Third Equation of motion

$\rm\:v{}^{2}=u{}^{2}+2aS$

Put the given values

$\sf\implies\:(12)^2=0+2\times0.1\:S$

$\sf\implies\:144=\dfrac{2}{10}\times\:S$

$\sf\implies\:144=\dfrac{1}{5}\times\:S$

$\sf\implies\:S=144\times5$

$\sf\implies\:S=720m$

Therefore, the distance travelled by the bus is 720m .

Answer 2

Given, that a bus starting from rest moves with a uniform acceleration of 0.1 m/s² for 2 minutes.

☯we need to find the speed acquired, and the

distance travelled by the bus.

So, here;

Initial velocity (u)= 0 m/s

Accelaration (a)= 0.1 m/s²

Time (t) = 2 min = 120 sec

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(A) To find the speed acquired, by first equation of motion;

⠀

$\star\;{\boxed{\sf{\purple {v=u+at }}}}$

Putting values,

$:\implies\sf v=0+0.1\times120$

$:\implies\sf v=12ms^{-1}$

$:\implies{\boxed{\frak{\pink{ v=12ms^{-1} }}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;the\: final\; velocity\; of \:the\; bus\; is\:\bf{12ms^{-1} }.}}}$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

(B) For finding the total distance travelled by the bus, we will apply third equation of motion;

$\star\;{\boxed{\sf{\purple {v{}^{2}=u{}^{2}+2aS}}}}$

Putting values,

$:\implies\sf (12)^2=0+2\times0.1\:S$

$:\implies\sf 144=\dfrac{2}{10}\times\:S$

$:\implies\sf 144=\dfrac{1}{5}\times\:S$

$:\implies\sf S=144\times5$

$:\implies\sf S=720m$

$:\implies{\boxed{\frak{\pink{ S=720\;m }}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;the\: distance\:travelled \:by\:the\; bus\; is\:\bf{720}.}}}$