Question

You are at a train station, standing next to the train at the front of the first car. The train starts moving with constant acceleration, and 9.0 s later the back of the first car passes you. Part A How long does it take after the train starts moving until the back of the seventh car passes you? All cars are the same length. Express your answer with the appropriate units.

Answer 1

23.81 seconds

Explanation:

Let the length of the car be 'x'

Acceleration of the car = a

Data provided in the question:

Initial speed of the car = 0 (as the train starts from rest)

Time taken (t) to cover distance of the first car i.e length of the car x = 9 s

Now,

from the Newton's equation of motion, we have

`s=ut+(1)/(2)at^2`

here,

s is the distance

a is the acceleration

t is the time

on substituting the values, we get

`x=0*9+(1)/(2)a*9^2`

or

x = 40.5a

or

a =
`(x)/(40.5)`

now,

the total length of the 7 cars = 7x

thus,

time taken to cover length 7x with acceleration
`(x)/(40.5)`, will be

from the Newton's equation of motion, we have

`s=uT+(1)/(2)aT^2`

here T is the time taken to cover back of the 7th car

on substituting the values, we get

`7x=0* T+(1)/(2)(x)/(40.5)T^2`

or

`7x=(1)/(2)(x)/(40.5)T^2`

or

7 × 2 × 40.5 = T²

or

T² = 567

or

T = 23.81 seconds