Crossing the Bridge

To calculate the time taken by the train to cross the bridge we have to first find the distance that the train has traveled. The length of the bridge is $300 m$ and the length of the train is $200 m$ . So, the train travels 300 m on the bridge and 200 m further because the train has to completely cross the bridge.

$S = 300 + 200 = 500 m$

Given : $Initial \space velocity \space (u) = 30 m/s$ and $Final \space velocity \space (v) = 50 m/s$

Now, we know that $V^2 - u^2 = 2aS$

$\implies a = \dfrac{v^2 - u^2}{2S} = \dfrac{2500 - 900}{2 \times 500} = \dfrac{1600}{1000} = 1.6 m/s^2$

So, the train moves with a constant acceleration of $1.6 m/s^2$ .

And also, v = u + at

$\implies t = \dfrac{v - u}{a} = \dfrac{50 - 30}{1.6} = \dfrac{20}{1.6} = \dfrac{100}{8} = 12.5$

Therefore, $\color{#20A900}\text{the train takes 12.5 seconds to cross the bridge .}$