Question

find the time taken, if the speed of a train increased from 72 km/hr to 90 km/hr for 234 km. leave your answer in seconds

Answer 1

Time taken = 10400 s

Step-by-step explanation:

Given:

Initial speed of the train,
`u=72\textrm{ km/h}=72* (5)/(18)=20\textrm{ m/s}`

Final speed of the train,
`v=90\textrm{ km/h}=90* (5)/(18)=25\textrm{ m/s}`

Displacement of the train,
`S=234\textrm{ km}=234* 1000=234000\textrm{ m}`

Using Newton's equation of motion,

`v - u = at\\a=(v-u)/(t)`

Now, using Newton's equation of motion for displacement,

`v^(2)-u^(2)=2aS`

Now, plug in the value of
`a=(v-u)/(t)` in the above equation. This gives,

`v^(2)-u^(2)=2* (v-u)/(t)* S\\(v+u)(v-u)=(2(v-u)S)/(t)\\t=(2(v-u)S)/((v+u)(v-u))\\t=(2S)/(v+u)`

Now, plug in 234000 m for
`S`, 25 m/s for
`v` and 20 m/s for
`u`. Solve for
`t`.

`t=(2S)/(v+u)\\t=(2* 234000)/(25+20)\\t=(468000)/(45)=10400\textrm{ s}`

Therefore, the time taken by the train is 10400 s.