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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