Question

The two velocities of a train with constant acceleration are $u$and $v$ respectively. What is the velocity at which the middle point of the train passes through the same point?

Answer 1

Step 1: Given Data:

The initial velocity of the train = $u$

The final velocity of the train = $v$

Step 2: Parameter to be calculated:

The velocity at which the middle point of the train passes through that same point.

Step 3: Formula used:

$v^2-u^2=2as$………(1)

Step 4: Calculation:

Considering the middle point of the train

Put $s^{\text{'}}=\frac{s}{2}$

and $v=v\text{'}$

Now equation (1) becomes

$2\left(v{\text{'}}^2-u^2\right)=2as$

Equating the above equation with (1)

$2\left(v{\text{'}}^2-u^2\right)=v^2-u^2$

After simplification

$v\text{'}=\sqrt{\frac{v^2+u^2}{2}}$

Hence, the velocity at which the middle point of the train passes through the same point is $v\text{'}=\sqrt{\frac{v^2+u^2}{2}}$.