Question

A train travels from rest at one station to rest at another in the same straight line distance it moves over the first part of the distance with an acceleration of F1 metre per second square and for the remainder with retardation of f2 metre per second square find time taken to complete the journey.​

Answer 1

Given that,

A train covers the first part of the distance with an acceleration

$a=F_{1}\ m/s^2$

A train covers the remainder part of the distance with an retardation

$a=F_{2}\ m/s^2$

Suppose, The total distance of complete journey is 2d.

Let the time of first part is t and reminder part is t'.

We need to calculate the velocity for first journey

Using equation of motion

$v=u+at$

Put the value into the formula

$v=0+F_{1}t$

We need to calculate the velocity for reminder journey

Using equation of motion

$v=u-at$

Put the value into the formula

$0=F_{1}t+F_{2}t'$

We need to calculate the total time for complete journey

Using formula of time

$t''=t+t'$

$t''=\dfrac{d}{v}+\dfrac{d}{v}$

Put the value into the formula

$t''=\dfrac{d}{F_{1}t}+\dfrac{d}{F_{1}t-F_{2}t'}$

Hence, The total time for complete journey is $\dfrac{d}{F_{1}t}+\dfrac{d}{F_{1}t-F_{2}t'}$