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Question Number 15100 by Tinkutara last updated on 07/Jun/17

A car A is travelling with a speed of 72  km/h on a straight horizontal road. It  is followed by another car B which is  moving with a velocity of 36 km/h.  When the distance between them is 25  km, the car A is given a deceleration of  2 ms^(−2) . After how much time will B  catch up with A?

$$\mathrm{A}\:\mathrm{car}\:{A}\:\mathrm{is}\:\mathrm{travelling}\:\mathrm{with}\:\mathrm{a}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{72} \\ $$$$\mathrm{km}/\mathrm{h}\:\mathrm{on}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{horizontal}\:\mathrm{road}.\:\mathrm{It} \\ $$$$\mathrm{is}\:\mathrm{followed}\:\mathrm{by}\:\mathrm{another}\:\mathrm{car}\:{B}\:\mathrm{which}\:\mathrm{is} \\ $$$$\mathrm{moving}\:\mathrm{with}\:\mathrm{a}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{36}\:\mathrm{km}/\mathrm{h}. \\ $$$$\mathrm{When}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{them}\:\mathrm{is}\:\mathrm{25} \\ $$$$\mathrm{km},\:\mathrm{the}\:\mathrm{car}\:{A}\:\mathrm{is}\:\mathrm{given}\:\mathrm{a}\:\mathrm{deceleration}\:\mathrm{of} \\ $$$$\mathrm{2}\:\mathrm{ms}^{−\mathrm{2}} .\:\mathrm{After}\:\mathrm{how}\:\mathrm{much}\:\mathrm{time}\:\mathrm{will}\:{B} \\ $$$$\mathrm{catch}\:\mathrm{up}\:\mathrm{with}\:{A}? \\ $$

Commented by Tinkutara last updated on 07/Jun/17

Commented by ajfour last updated on 07/Jun/17

   s_(rel) =−10(5+5(√2))+(1/2)(2)(5+5(√2))^2        =−50−50(√2)+25+50+50(√2)       =25 m.

$$\:\:\:{s}_{{rel}} =−\mathrm{10}\left(\mathrm{5}+\mathrm{5}\sqrt{\mathrm{2}}\right)+\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{2}\right)\left(\mathrm{5}+\mathrm{5}\sqrt{\mathrm{2}}\right)^{\mathrm{2}} \\ $$$$\:\:\:\:\:=−\mathrm{50}−\mathrm{50}\sqrt{\mathrm{2}}+\mathrm{25}+\mathrm{50}+\mathrm{50}\sqrt{\mathrm{2}} \\ $$$$\:\:\:\:\:=\mathrm{25}\:{m}. \\ $$

Answered by sandy_suhendra last updated on 07/Jun/17

the distance between the two cars is impossible 25 km

$$\mathrm{the}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{the}\:\mathrm{two}\:\mathrm{cars}\:\mathrm{is}\:\mathrm{impossible}\:\mathrm{25}\:\mathrm{km}\:\:\:\:\: \\ $$

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