Question

a train is traveling at 90 km/h the Breck are applied so as to produce a uniform acceleration of -0.5 m/s find how for the train gas before it stop​

Answer 1

Correct Question-

A train is travelling at 90 km/h, the brake are applied so as to produce a uniform acceleration of -0.5 m/s². Find how far the train goes before it stop​s.

Given:

Initial velocity of train,u= 90 km/h

Final velocity of train,v= 0 km/h

(Since, train stops Finally)

Acceleration of train,a= -0.5 m/s²'

To Find:

Distance travelled by train after the brakes were applied

Solution:

We know that,

• According to third equation of motion for constant acceleration,

$\pink{\underline{\boxed{\bf{v^{2}-u^{2}=2as}}}}$

where,

v is final velocity

u is initial velocity

a is acceleration

s is displacement

$\rule{190}{1}$

It is given that,

$\longrightarrow\rm{u=90\ km/h=90\times\dfrac{5}{18}\ m/s=25\ m/s}$

$\longrightarrow\rm{v=0\ km/h=0\times\dfrac{5}{18}\ m/s=0\ m/s}$

$\rule{190}{1}$

Let the distance covered by train before it stops after applying brakes be 's'

Also, on applying third equation of motion on train, we get

$\longrightarrow\rm{v^{2}-u^{2}=2as}$

$\longrightarrow\rm{(0)^{2}-(25)^{2}=2(-0.5)s}$

$\longrightarrow\rm{-625=-s}$

$\longrightarrow\rm{-s=-625}$

$\longrightarrow\rm\green{s=625\ m}$

Hence, the distance covered by train after the brakes were applied is 625 m.