# http://www.enotes.com/homework-help/train-100-metres-long-starts-from-rest-station-442022?qadded=1 Find the acceleration of the train and show that the total distance travelled is  302.5 metres,...

Find the acceleration of the train and show that the total distance travelled is  302.5 metres, when the rear of the train is at B.

ishpiro | Certified Educator

Consider the following quantities:

a is the acceleration of the train

is the velocity of the train when its head passes the signal post B.

Then,

`V_1 = at`  , where t is the time it took the head of the train to reach signal post B.

Since the velocity of the train increased from to 11 m/s in 10 seconds during which the train passed the signal post B,

`11 = V_1 + a*10` .

Since the length of the train is 100 m,

`100 = V_1*10 + (a*10^2)/2`

These three equations can be used to find a and t.

`11 = V_1 + 10a`

`100 = 10V_1 + 50t`

The second equation is equivalent to `10 = V_1 + 5a`

From the first equation, `V_1 = 11 - 10a`

Plugging this into the second equation, get

`10 = 11 - 10a+5a = 11 - 5a`

From here `a = 1/5 m/s^2`

Then `V_1 = 11 - 10a = 11 - 10* 1/5 = 9 m/s`

Now from the very first equation we could find the time it took the head of the train to reach signal post B:

`t=V_1/a = 11/(1/5) = 55 s`

That means the time it took the rear of the train to reach signal post B is 10 seconds greater: 55 s + 10 s = 65 s

That means the total distance traveled by the time the rear of the train reaches B is

`d = at^2/2 = (1/5)*(65)^2 / 2 = 422.5 m`

This is the distance traveled by the head of the train. The rear of the train traveled 100 m less:

422.5 m - 100 m = 322.5 meters