Question

A train starts from rest.If it's velocity after 6 minutes is 90 km/ hr,calculate it's acceleration and distance travelled by it.​

Answer 1

The train has an acceleration of 900km/h² and has travelled 4.5km.

Step-by-step explanation:

This question utilises SUVAT equations, so let's break down how to work it out.

For Acceleration

The general formula for this is
`v=u+at` and when we rearrange it in terms of acceleration we get
`a=(v-u)/(t)` (where v = final velocity in km/h, u = initial velocity in km/h, t = time in hours (h) and a = acceleration in km/h²).

Therefore:

`v=90\;\;\;\;\;\;u=0\;\;\;\;\;\;t=6 mins=0.1h\\\\\therefore a=(90-0)/(0.1) =900km/h^2`

Therefore our answer is 900km/h².

For Distance

We can calculate the distance (or rather displacement, which is shown by s, and this context is measured in km) by a range of equations in the SUVAT category however we will use
`s=ut+(1)/(2) at^2` since it is easier (as initial velocity is 0km/h).

Therefore:

`t=6mins=0.1h\;\;\;\;\;\;u=0km/h\;\;\;\;\;\;a=900km/h^2\\\\\therefore s=(0*0.1)+(1)/(2)(900*0.1^2)=4.5km`

Therefore our answer is 4.5km.

Hope this helps!!!