Question

A train travelling at 20ms-1acecelerates at 0.5ms-2 for 30 s how far will it travel in this time

Answer 1

Given :

• Initial velocity ( u ) = 20 m/s

• Acceleration ( a ) = 0.5 m/s²

• Time ( t ) = 30 sec

To Find :

• Distance travelled by train in 30 sec

Solution :

By using 2nd equation of motion

$\large\boxed{ \boxed{\sf\blue{S = ut+ \frac{1}{2}{at}^{2}}}} \\ \\ \implies \sf s = 20 \times 30 + \frac{1}{2} \times 0.5 \times {(30)}^{2} \\ \\ \implies \sf s =600 + \frac{1}{2} \times 0.5 \times 900 \\ \\ \implies \sf s =600 + \frac{1}{2} \times450 \\ \\ \implies \sf s =600 + 225 \\ \\ \large\implies \boxed{ \boxed{\sf \green{s =825 \: m}}}$

Train will travel 825 m in 30 sec

Answer 2

${\bold{\pink{\underline{\green{G}\purple{iv}\orange{en}\red{:-}}}}}$

• $\bf\:Initial\:velocity\:(u)=20\:m/s$

• $\bf\:Acceleration\:(a)=0.5\:m/{s}^{2}$

• $\bf\:Time\:(t)=30\:sec$

${\bold{\pink{\underline{\pink{To}\:\purple{Fin}\blue{d}\red{:-}}}}}$

☛ Distance travelled=?

${\bold{\pink{\underline{\red{So}\purple{lut}\green{ion}\orange{:-}}}}}$

$\bf\boxed\star\pink{\underline{\underline{{Using\:Second\:equation\:of\:motion}}}}$

$\bf\:s=ut+\dfrac{1}{2}a{t}^{2}$

$\bf\:s=20\times\:30+\dfrac{1}{2}\times\:0.5\times\:{(30)}^{2}$

$\bf\:s=20\times\:30+\dfrac{1}{2}\times\:0.5\times\:30\times\:30$

$\bf\:s=600+225$

$\bf\red{{s=825\:m}}$

☛ Other equation of motion

$\bf\green{{v=u+at}}$

$\bf\purple{{{v}^{2}={u}^{2}+2as}}$