Question

a train starts from rest and moves with a acceleration 2 m/s for half a minute .the brakes are than applied and the trains are rest in ine minute .find the total distance moved by the train​

Answer 1

$\huge{\mathfrak{Question:-}}$

A train starts from rest and moves with a acceleration 2 m/s for half a minute .the brakes are than applied and the trains are rest in ine minute. Find the total distance moved by the train​.

$\huge{\mathfrak{Solution:-}}$

$\sf{The\;distance\;covered\;by\;train\;in\;the\;first\;halfe\;minute,}$

$\sf{s_{1}=u_{1}t_{1}+\frac{1}{2}a_{1}t_{1}^{2}}$

$\sf{\implies 0+\frac{1}{2}\times 2\times 30^{2}}$

$\sf{\implies 900\;m}$

$\sf{The\;velocity\;after\;30\;s,}$

$\sf{u_{2}=u_{1}+a_{1}t_{1}}$

$\sf{\implies 0+2\times 30}$

$\sf{\implies 60\;m/s}$

$\sf{Let\;us\;find\;the\;acceleration\;in\;second\;half\;minute\;by\;using\;equation\;of\;motion,}$

$\sf{v_{2}=u_{2}+a_{2}t_{2}}$

$\sf{\implies 0=60+a_{2}\times 30}$

$\sf{\implies a_{2}=-2\;m/s^{2}}$

$\sf{The\;maximum\;speed\;is\;60\;m/s}$

$\sf{Therefore,\;the\;position\;of\;the\;train\;at\;30\;m/s}$

$\sf{v_{3}^{2}=u_{1}^{2}+2a_{1}s_{3}}$

$\sf{\implies 30^{2}=0+2\times 2\times s_{3}}$

$\sf{\implies s_{3}=900/4}$

$\sf{\implies s_{3}=225\;m}$

Let us find the position of the train when the train is decelerating and reaches speed 30 m/s.

$\sf{v_{4}^{2}=u_{2}^{2}+2a_{2}s_{4}}$

$\sf{\implies 30^{2}=60^{2}-2\times 2\times s_{4}}$

$\sf{\implies s_{4}=\frac{60^{2}-30^{2}}{4}}$

$\sf{\implies s_{4}=675\;m}$

$\sf{The\;total\;distance\;covered=s_{1}+s_{4}}$

$\sf{The\;total\;distance\;covered=900+675}$

$\boxed{\sf{The\;total\;distance\;covered=1575\;m}}$

Answer 2

$\huge\bold\red{Hope \: it \: helps} \\ \\ \\ \huge\green{Have \: a \: cheerful \: day}$