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Question

A train $$200 m $$ long crosses a bridge $$300 m $$ long. It enters the bridge with a speed of $$3 ms^{-1} $$ and leaves it with a speed of $$ 5 ms^{-1} $$. What is the time taken to cross the bridge?


Solution

The acceleration is given as,

$$a = \dfrac{{{v^2} - {u^2}}}{{2s}}$$

$$ = \dfrac{{{{\left( 5 \right)}^2} - {{\left( 3 \right)}^2}}}{{2 \times 500}}$$

$$ = \dfrac{{16}}{{1000}}\;{\rm{m/}}{{\rm{s}}^{\rm{2}}}$$

The time taken to cross the bridge is given as,

$$t = \dfrac{{v - u}}{a}$$

$$ = \dfrac{{5 - 3}}{{\dfrac{{16}}{{1000}}}}$$

$$ = 125\;{\rm{s}}$$

Thus, the time taken to cross the bridge is $$125\;{\rm{s}}$$.


Physics

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