Question

a train starts at rest with acceleration of 0.5ms-2 find speed in kmh when it has moved through 100m
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Answer 1

Answer:

use the third equation of motion

v2-u2=2as

v=0.5

u=0

s=100m

a=find out

Answer 2

Given-

• Acceleration = 0.5m/s²
• Initial speed of train = 0m/s
• Distance Covered by the train = 100m

Find-

Speed in km/h-?

   

Formulas to be used-

• $\boxed{\bf{ v= \dfrac{s}{t} }}$

• $\boxed{\bf{ S= ut + \dfrac{1}{2} at^2 }}$

where,

s= Distance,

u= initial speed

t= time

v= speed

a= acceleration

     

SoLution-

At first find time,

by using 2nd equation of motion,

$\sf{ S= ut + \dfrac{1}{2} at^2 }$

put given values in the formula we get,

$\sf{\implies 100 = 0 \times t + \dfrac{1}{2} \times 0.5 \times t^2 }$

$\sf{\implies 100 = \dfrac{1}{2} \times 0.5 \times t^2}$

$\sf{\implies 100 \times 2 = 0.5 \times t^2 }$

$\sf{ \implies 200 = 0.5 \times t^2 }$

$\sf{\implies \dfrac{200}{0.5} = t^2}$

$\sf{\implies t^2= \dfrac{200\times 10}{5} }$

$\sf{\implies t^2 = \dfrac{2000}{5} = 400 }$

$\sf{\implies t= \sqrt{400} }$

$\sf{\implies t= 20sec}$

 

Now,

Using speed formula,

$\sf{V= \dfrac{S}{t} }$

$\sf{ \implies V= \dfrac{100}{20} }$

$\sf{\implies V= \dfrac{10m}{2s} = 5m/s }$

 

So, the Speed of the train is 5m/s

 

According to question we should find speed into km/h

 

we know,

$\sf{ 1km= 1000m}$

$\sf{1hr= 3600sec}$

So,

$\sf {\dfrac{1km}{1hr} = \dfrac{1000m}{3600s} = \dfrac{5m}{18s} }$

$\sf{\implies \dfrac{18}{5}km/h = 1m/s}$

$\sf{ \implies 5\times \dfrac{18}{5} km/h = 5m/s}$

$\sf{\implies 5m/s = 18km/h}$

$\bf{\underline{\orange{ Hence, Speed \ of \ train \ is \ 18km/h. }}}$