train normally travels at a uniform speed of $$72V$$,$$km/h$$ on a long stretch of straight level track. On a particular day, the train was forced to make a $$2.0$$ minute stop at a stationalong this track. If the train decelerates at a uniform rate of $$1.0$$ $$m/s2$$ and accelerates at a rate of $$0.50$$ $$m/s2$$, how much time is lost in stopping at the station?

Question

Infinity Learn · Accepted Answer

$$Case-I$$: Actual time spent in $$decelerating=v$$−$$ua=0$$−$$20$$−$$1.0=20sDistance$$ travelled in $$decelerating=20$$×$$20$$−$$12$$×$$1$$×$$202=400$$−$$200=200mTime$$ that train will have taken if it had travelled uniformlywith $$20$$ $$m/s$$ for $$200$$ m $$=20020=10sExtra$$ time spent in decelerating $$=$$ $$20$$ $$-$$ $$10$$ $$=$$ $$10$$ $$sCase-II$$: Actual time spent in $$accelerating=v$$−$$ua=20$$−$$00.5=40sDistance$$ travelled in these $$40$$ $$s=0$$×$$40+12$$×$$0.5$$×$$402=400mTime$$ that the train will have taken if travelled uniformly with $$20$$ $$m/s=40020=20s$$ Extra time lost due to acceleration $$=40$$−$$20=20s$$ Total extra time $$=10s+2min+20s=2min30s$$

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