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        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?
4 years ago

22 Points
							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 + atvmax = 0 + $\alpha$t1Vmax = $\alpha$t1    …......(1)Similarly,Taking second part,0 = vmax - $\beta$t2-vmax = -$\beta$t2vmax = $\beta$t2  …...........(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 hrsSubstituting the values in equation (3) we get,0.5 = 0.4 vmax + 0.2 vmax / 0.4*0.2vmax = 0.04When we plot the velocity – time graph we get a traingle with its peak as vmax ( that is height ) and base as 0.5Since 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

4 years ago
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### Course Features

• 110 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions