A train starts from rest from a stations with acceleration $0.2 m / s^{2}$ on a straight track and then comes to rest after attaining maximum speed on another station due to retardation $0.4 m / s^{2}$ .IF total time spent is half an hour,then distance between two stations is [Neglect length of train]

Open in App

Solution

Case I:
Train accelerates with $a = 0.2 m / s^{2}, t = t_{1}$ and $v = v_{1}$

$v = u + a t a n d v_{1} = 0.2 t_{1} o r t_{1} = 0.2 \frac{v_{1}}{2} \dots (1)$

$s = u t + 0.5 a t^{2}$

Case II:

$v_{2} = v_{1} + a_{2} t_{2}$ (train is retarding and $s = s_{1}$ )

$s_{1} = 0.5 x 0.2 x t_{1}^{2}$

$v_{2} = v_{1} + a_{2} t_{2}$

$0 = v_{1} + 0.4 t_{2}$

$t_{2} = \frac{- v_{1}}{0.4} \dots (2)$

$s_{2} = v_{1} t_{2} + (\frac{1}{2}) x a_{2} t_{2}^{2}$

$t = t_{1} + t_{2} = 30 m i n = 1800$

$t_{1} = 1200 s$ and $t_{2} = 600 s$

Substituting a, v and t in equation(1) and (3), we get

$s_{1} = 144 k m$ and $s_{2} = 72 k m$

Total distance $s = s_{1} + s_{2}$

$s = 216 k m$

Suggest Corrections

Similar questions

Q. A train starts from rest from a station with acceleration

0.2

sec on a striaght track and then comes to rest after attianing maximum speed on another station due to retardation if total time spent is half is half an hour then, distance between two stations is:

Q. A train starts from rest and moves with a constant acceleration of

2.0 m / s^{2}

for half a minute. The brakes are then applied and the train comes to rest in one minute after applying breaks. Find (a) the total distance moves by the train, (b) the maximum speed attained by the train and (c) the position(s) of the train at half the maximum speed. (Assume retardation to be constant).

Q. Between two stations a train starting from rest first accelerates uniformly, then moves with constant velocity and finally retards uniformly to come to rest. If the ratio of the time taken is 1:8:1 and the maximum speed attained is 60km/hr, then what is the average speed over the whole journey?

The distance between the two stations was $550 k m$ . Two trains start at same time from the two station on parallel track to cross one another .The speed of one train is $10 k m$ per hour more than the other . If after $3$ hours the train reaches $40 k m$ , find their speed?

Q. A train starts from station A with a uniform acceleration

a_{1}

for some distance and then goes with uniform retardation

a_{2}

for some more distance to come to rest at station B. The distance between stations A and B is 4 km and the train takes 1/15 h to complete this journey. If accelerations are
in km per minute, find value of

\frac{1}{a_{1}} + \frac{1}{a_{2}}

Join BYJU'S Learning Program

A train starts from rest from a stations with acceleration 0.2m/s2 on a straight track and then comes to rest after attaining maximum speed on another station due to retardation 0.4m/s2.IF total time spent is half an hour,then distance between two stations is [Neglect length of train]