Question

7. A train passes 300 m long platform in 30 s and it crosses a signal on the station in 12 s. Find:
a) the speed of the train in km/h.
b) the length of the train.​

Answer 1

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\huge\tt\purple{♬•Answer}$

$\huge\tt{a) 16.6m/s}$

$\huge\tt{b) 200m}$

A<_____ >B<___________>C

Let the length of train be x(AB)

Here BC is the 300km long platform and AB is the train.... Of length x, so train will pass the platform completely when the last coach will pass the platform.... So the total distance the train covered while passing the platform is

AB+BC or

X+300

Now, according to formula

Distance= speed x time

X+300=speed x 30s. (given)

Speed= (x+300)/30______(i)

Now, see the second case....

[A] <-------x--------->

The train crosses a signal, it will cross it completely after its last coach will pass the signal.. So the distance travelled is x

Now, again use the formula:

Distance= speed x time

X=speed x 12s. (given)

Speed= x/12 _____(ii)

Now, equating (i) and (ii)

(x+300)/30=x/12

12x+3600=30x

3600=18x

X=3600/18=200

So the length of train is 200m

From (ii), speed =x/12 = 200/12= 50/3=16.6m/s