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Question Number 72560 by Umar last updated on 30/Oct/19

Commented by Umar last updated on 30/Oct/19

solve 3 and 4 pls

$$\mathrm{solve}\:\mathrm{3}\:\mathrm{and}\:\mathrm{4}\:\mathrm{pls} \\ $$

Commented by TawaTawa last updated on 30/Oct/19

(3i)  We have,      u  =  10m/s,        v  =  15m/s,     a  =  1m/s^2 .  The time (t)  =  ?             a  =  ((v − u)/t)  ∴             1  =  ((15  − 10)/t)  ∴              t  =  5s  (3ii)                 v^2   =  u^2  + 2as  ∴              15^2   =  10^2  + 2(1)s  ∴              225  =  100 + 2s  ∴                    2s   =   225 − 100  ∴                    2s   =   125  ∴                      s  =  ((125)/2)  ∴                      s  =  62.5m  (3iii)                       s  =  (((v + u)/2)).t  ∴                     v^2   =  u^2  + 2as  ∴                     v^2   =  0^2  + 2(1)(100)  ∴                     v^2   =  0 + 200  ∴                     v^2   =   200  ∴                       v  =   (√(200))  ∴                       v  =   14.14 m/s

$$\left(\mathrm{3i}\right) \\ $$$$\mathrm{We}\:\mathrm{have},\:\:\:\:\:\:\mathrm{u}\:\:=\:\:\mathrm{10m}/\mathrm{s},\:\:\:\:\:\:\:\:\mathrm{v}\:\:=\:\:\mathrm{15m}/\mathrm{s},\:\:\:\:\:\mathrm{a}\:\:=\:\:\mathrm{1m}/\mathrm{s}^{\mathrm{2}} . \\ $$$$\mathrm{The}\:\mathrm{time}\:\left(\mathrm{t}\right)\:\:=\:\:? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{a}\:\:=\:\:\frac{\mathrm{v}\:−\:\mathrm{u}}{\mathrm{t}} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}\:\:=\:\:\frac{\mathrm{15}\:\:−\:\mathrm{10}}{\mathrm{t}} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{t}\:\:=\:\:\mathrm{5s} \\ $$$$\left(\mathrm{3ii}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{v}^{\mathrm{2}} \:\:=\:\:\mathrm{u}^{\mathrm{2}} \:+\:\mathrm{2as} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{15}^{\mathrm{2}} \:\:=\:\:\mathrm{10}^{\mathrm{2}} \:+\:\mathrm{2}\left(\mathrm{1}\right)\mathrm{s} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{225}\:\:=\:\:\mathrm{100}\:+\:\mathrm{2s} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2s}\:\:\:=\:\:\:\mathrm{225}\:−\:\mathrm{100} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2s}\:\:\:=\:\:\:\mathrm{125} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{s}\:\:=\:\:\frac{\mathrm{125}}{\mathrm{2}} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{s}\:\:=\:\:\mathrm{62}.\mathrm{5m} \\ $$$$\left(\mathrm{3iii}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{s}\:\:=\:\:\left(\frac{\mathrm{v}\:+\:\mathrm{u}}{\mathrm{2}}\right).\mathrm{t} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{v}^{\mathrm{2}} \:\:=\:\:\mathrm{u}^{\mathrm{2}} \:+\:\mathrm{2as} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{v}^{\mathrm{2}} \:\:=\:\:\mathrm{0}^{\mathrm{2}} \:+\:\mathrm{2}\left(\mathrm{1}\right)\left(\mathrm{100}\right) \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{v}^{\mathrm{2}} \:\:=\:\:\mathrm{0}\:+\:\mathrm{200} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{v}^{\mathrm{2}} \:\:=\:\:\:\mathrm{200} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{v}\:\:=\:\:\:\sqrt{\mathrm{200}} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{v}\:\:=\:\:\:\mathrm{14}.\mathrm{14}\:\mathrm{m}/\mathrm{s} \\ $$$$ \\ $$

Commented by TawaTawa last updated on 30/Oct/19

(4)               v^2   =  u^2  + 2as  ∴        20^2   =  50^2  + 2(− 10).s  ∴        400   =   2500  −  20s  ∴        400   −  2500  =  −  20s  ∴        −  2100  =  −  20s  ∴           s   =  ((− 2100)/(− 20))  ∴           s   =  105m

$$\left(\mathrm{4}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{v}^{\mathrm{2}} \:\:=\:\:\mathrm{u}^{\mathrm{2}} \:+\:\mathrm{2as} \\ $$$$\therefore\:\:\:\:\:\:\:\:\mathrm{20}^{\mathrm{2}} \:\:=\:\:\mathrm{50}^{\mathrm{2}} \:+\:\mathrm{2}\left(−\:\mathrm{10}\right).\mathrm{s} \\ $$$$\therefore\:\:\:\:\:\:\:\:\mathrm{400}\:\:\:=\:\:\:\mathrm{2500}\:\:−\:\:\mathrm{20s} \\ $$$$\therefore\:\:\:\:\:\:\:\:\mathrm{400}\:\:\:−\:\:\mathrm{2500}\:\:=\:\:−\:\:\mathrm{20s} \\ $$$$\therefore\:\:\:\:\:\:\:\:−\:\:\mathrm{2100}\:\:=\:\:−\:\:\mathrm{20s} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\mathrm{s}\:\:\:=\:\:\frac{−\:\mathrm{2100}}{−\:\mathrm{20}} \\ $$$$\therefore\:\:\:\:\:\:\:\:\:\:\:\mathrm{s}\:\:\:=\:\:\mathrm{105m} \\ $$

Commented by TawaTawa last updated on 30/Oct/19

Sir  MrW  please check.

$$\mathrm{Sir}\:\:\mathrm{MrW}\:\:\mathrm{please}\:\mathrm{check}. \\ $$

Commented by Umar last updated on 30/Oct/19

Thank u sir

$$\mathrm{Thank}\:\mathrm{u}\:\mathrm{sir} \\ $$

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