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# A train is travelling at a speed of 90 km /h. Brakes are applied so as to produce a uniform acceleration of $$–0.5 m /s ^2$$ . Find how far the train will go before it is brought to rest.

Given, initial velocity= 90 km/h = $$90 ×$$ $$5 \over 18$$ $$= 25 \ m/s$$
final velocity = 0 m/s
{ as train is brought to rest}

a = $$–0.5 m /s ^2$$

By the third motion equation,

$$\therefore v^2 - u^2 = 2as$$
$$\Rightarrow 0^2 \ - \ 25^2 \ = \ 2 ×(-0.5) s$$ $$\Rightarrow s = 625 \ m$$

$$\therefore$$ The train will travel 625 meters before it is brought to rest.