Question:
A metro trains starts from rest and in $5 \,s$ achieves $108 \,km/h$. After that it moves with constant velocity and comes to rest after travelling $45 \,m$ with uniform retardation. If total distance travelled is $395 \,m$, find total time of travelling.
A metro trains starts from rest and in $5 \,s$ achieves $108 \,km/h$. After that it moves with constant velocity and comes to rest after travelling $45 \,m$ with uniform retardation. If total distance travelled is $395 \,m$, find total time of travelling.
Updated On: Jun 17, 2022
- 12.2s
- 15.3s
- 9s
- 17.2s
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The Correct Option is D
Solution and Explanation
Given $v = 108 \, kmh^{-1} = 30 \,ms^{- 1} $
From first equation of motion
v = u + at
hence $ 30=0+a\times 5 $
(hence $u=0)$
or $ a=6\, ms^{-2} $
So, distance travelled by metro train in $5\, s$
$ s_1=\frac{1}{2}at^2=\frac{1}{2}\times (6)\times (5)^2=75\, m $
Distance travelled before coming to rest $=45 \,m $
So, from third equation of motion
$ o^2=(30)^2-2a' \times 45 $
or a' $ =\frac{30 \times 30 }{2 \times 45 }=10\, ms^{-2} $
Time taken in travelling $45 \,m$ is
$ t_3=\frac{30}{10}=3\, s $
Now, total distance = 395 \,m
i,e $75 + y + 45 = 395\, m$
or $s'=395 -(75 +45)=275 \,m$
$ \therefore $ $ t_2=\frac{275}{30}=9.2\,s $
Hence, total time taken in whole journey
$= t_1+t_2+t_3 $
$=5+9.2+3$
$=17.2\,s$
From first equation of motion
v = u + at
hence $ 30=0+a\times 5 $
(hence $u=0)$
or $ a=6\, ms^{-2} $
So, distance travelled by metro train in $5\, s$
$ s_1=\frac{1}{2}at^2=\frac{1}{2}\times (6)\times (5)^2=75\, m $
Distance travelled before coming to rest $=45 \,m $
So, from third equation of motion
$ o^2=(30)^2-2a' \times 45 $
or a' $ =\frac{30 \times 30 }{2 \times 45 }=10\, ms^{-2} $
Time taken in travelling $45 \,m$ is
$ t_3=\frac{30}{10}=3\, s $
Now, total distance = 395 \,m
i,e $75 + y + 45 = 395\, m$
or $s'=395 -(75 +45)=275 \,m$
$ \therefore $ $ t_2=\frac{275}{30}=9.2\,s $
Hence, total time taken in whole journey
$= t_1+t_2+t_3 $
$=5+9.2+3$
$=17.2\,s$
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Concepts Used:
Motion in a straight line
The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
- Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
- Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.