Question

train moving with uniform acceleration has a velocity of 30 kilometre per hour at A and 60 km per hour at B find its velocity and the middle of the interval and also the velocity Midway between a and b​

Answer 1

Answer:

velocity at middle of the interval or midway of the interval = v = 47.43 km/h.

Explanation:

Given,

* velocity at A = u = 30 km/h

* velocity at B = v = 60 km/h

let 'a' and 's' be the acceleration of the block and displacement between the points A and B.

Therefore, from Point A to B,

$v^2\ =\ u^2\ +\ 2as\\\Rightarrow 2as\ =\ v^2\ -\ u^2\\\Rightarrow 2as\ =\ 60^2\ -\ 30^2\\\Rightarrow 2as\ =\ 2700\,\,\,\,\,\,\,\,\,\,\,\,\,\,eqn (1)$

Now at the middle of the interval, displacement = s/2

Let $v_m$ be the velocity of the train at the middle of the interval,

therefore,

$v_m^2\ =\ u^2\ +\ 2as/2\\\Rightarrow v_m^2\ =\ 30^2\ +\ 2700/2\\\Rightarrow v_m\ =\ \sqrt{900\ +\ 1350}\\\Rightarrow v_m\ =\ 47.43\ km/s.$

And the velocity at the midway between a and b is also same of the middle of the interval.