Question

a metro train starts from rest and in five seconds achieves 108km/h. After that it moves with constant velocity and comes to rest after travelling 45m with uniform retardiation. If total distance is 395m, then find the total time of travelling of the metro. (Ans-17.2s but how??)

Answer 1

First, lets convert 108km/h to m/s.It is equal to 30m/s. 

The motion of the train can be split up into three intervals. It first traveled for 5 seconds until it reaches 30m/s, and the moves at contant velocity for a certain time, and then decelerates for 45 meters until it slows down and stops. 

calculate the distance it travel initially for that 5 seconds: 

d=(V1 + V2)/2 * t 
d= (0 + 30)/2 * 5 
d= 15(5) 
d= 75m 

now we know that the train initially traveled 75m, and then went at constant velocity for a certain time, and then stopped in 45m. Since the total distance the train traveled is 395m, the distance it traveled while moving at constant velocity is 395 - (45 + 75)=275m. 

Now we can calculate the time the train moved at constant velocity: 

d=(V1 + V2)/2 * t 
275= (30 + 30)/2 * t 
275=30t 
t=9.2s 

Next, calculate the time it took the train to decelerate and stop. 

d=(V1 + V2)/2 * t 
45=(30 + 0)/2 *t 
45=15t 
t=3s 

Now add up all the times: 

5s + 9.2s + 3s =17.2s 

So the total traveling time of the metro is 17.2 seconds.

Answer 2

Answer:

The total time of travelling of the metro is 17.2 sec.

Explanation:

Given that,

Total distance D= 395 m

A metro train starts from rest and in five seconds achieves 108 km/h.

Initial velocity u = 0

Final velocity v = 108 km/h

Time t= 5 s

Using equation of motion

$v= u+at$

$a= \dfrac{30}{5}$

$a = 6 m/s^2$

The distance covered by the train is

Using equation of motion

$s= ut+\dfrac{1}{2}at^2$

$s= 0+\dfrac{1}{2}\times6\times5\times5$

$s= 75 m$

The total distance covered by the metro train

$d= 395-75-45=275\ m$

The time is

$t'= \dfrac{275}{30}$

$t'= 9.16 s$

After that it moves with constant velocity and comes to rest after travelling 45 m with uniform retardation.

$v= 0$

$u = 30 m/s$

Using equation of motion

$v=u-at$

$a=\dfrac{30}{t''}$

The time is

$s= ut''-\dfrac{1}{2}at''^2$

$45=30t''-\dfrac{1}{2}\times30t''\timest''^2$

$t''=3\ sec$

The total time is

$T= t+t'+t''$

$=5+9.16+3$

$T= 17.16=17.2\ sec$

Hence, The total time of travelling of the metro is 17.2 sec.