0

Guest

Courses New

A train starts from rest from a station with acceleration 0.2 on a stright line and then comes to rest after attaining maximum speed on another station due to retardation 0.4. if total time spent is half an hour, then distance between two stations is?

A train starts from rest from a station with acceleration 0.2 on a stright line and then comes to rest after attaining maximum speed on another station due to retardation 0.4. if total time spent is half an hour, then distance between two stations is?

Grade:12th pass

1 Answers

Paarth Arkadi
22 Points
8 years ago
Since the units of accleration / retardation are not given i assume it to be km/h2.
This is a case of 1-D motion.
Let the accleration and retardation of the train be \alpha and \beta respectively.
The train starts from rest and attains a velocity vmax then it starts retarding and finally comes to rest.
Hece the motion can be divided into two parts accleration and retardation.
Taking the first part,
u (initial velocity) = 0                  …. ( since train starts from rest)
v = vmax                                         …..( final velocity)
time = t1                                         …..( total time = t1 + t2 )
By using the equation,
v = u + at
vmax = 0 + \alphat1
Vmax = \alphat1    …......(1)
Similarly,
Taking second part,
0 = vmax - \betat2
-vmax = -\betat2
vmax = \betat2  …...........(2)
From eq (1) and (2),
t1 = and  t2 = vmax / \beta
 
Total time = t = t1 + t2 = vmax /\alpha  + vmax / \beta   
Therefore , t = \beta vmax + \alpha vmax / \alpha\beta …................(3)
Since it is given that total time (t) = 0.5 hrs
Substituting the values in equation (3) we get,
0.5 = 0.4 vmax + 0.2 vmax / 0.4*0.2
vmax = 0.04
When we plot the velocity – time graph we get a traingle with its peak as vmax ( that is height ) and base as 0.5
Since the area under velocity – time graph gives displacement ( in this case same as distance ) we have,
distance / displacement = ½ * vmax * total time (t)
                                           = ½ * 0.04 * 0.5
                                           = 0.01 km or 10 m
 

Think You Can Provide A Better Answer ?

Other Related Questions on Mechanics

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More