Question

A train is travelling at the speed of 90 km h-¹ . brakes are applied so as to produce a uniform acceleration of -0.5 m S-². find how far the train will go before it is brought to rest.​

Answer 1

$\large\sf \underline \bold{ \underline{Given :}}$

Initial velocity of train = 90km/h

Final velocity= 0 ( break applied )

Acceleration (retardation)= -0.5m/s^2

$\large\sf \underline \bold{ \underline{To \: find :}}$

Distance covered by the train before brought in rest .

$\large\sf \underline \bold{ \underline{solution :}}$

Using third equation of motion

$\boxed{\sf v^2= u^2+2as}$

v= final velocity

u= initial velocity

a= acceleration

s= distance

Convert initial speed of car into m/s

$\bullet\sf 1 \ km/h = \dfrac{5}{18}\ m/s\\ \\ \implies\sf \cancel{90}\times \dfrac{5}{\cancel{18}}= 5\times 5\\ \\ \implies\sf u= 25m/s\\ \\ \implies\sf v= 0$

Now find distance

$\implies\sf (0)^2= (25)^2+2\times (-0.5)\times s\\ \\ \implies\sf 0= 625 -1s\\ \\ \implies\sf -625= -1s\\ \\ \implies\sf \cancel{\dfrac{-625}{-1}}= s\\ \\ \implies\sf 625= s$

$\underline{\bigstar{\sf\ \ Distance \ covered \ by \ train = 625m}}$

Answer 2

Answer:

♧$\bold{Given:-}$

• A train is travelling at a speed of 90km h^-1
• Brakes are applied so as to produce a uniform acceleration of -0.5m /s^2.

♧$\bold{To prove:-}$

• Find how far train will go before it is brought to rest.

♧$\bold{Explanation:-}$

• Here we should find how the far the train will go before it is brought to rest
• So,

• Here we should use the third equation of motion to get the perfect answer.

♧$\bold{ {v}^{2} = {u }^{2} +2 as}$

• If we should enter to the question we should convert initial speed of train to m/s So,

• $= (90 \times \frac{5}{18} )m \: per \: sec = 5 \times 5 = 25 \: m \: per \: sec$

• Here,
• u=25 m/s= initial velocity
• v=0m/s=final velocity
• a=-0.5m/s^2=acceleration
• s=distance

• ♧Now applying all the values we get that,

• $( {0}^{2} ) = {25}^{2} + 2 \times ( - 0.5)s$
• $s = 625m$

$therefore \: train \: \: the \: will \: go \: before \: it \: is \: brought \: to \: rest \: is \: 625m$

♧Hope it helps u mate.

♧Thank you