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Question Number 83606 by MJS last updated on 04/Mar/20

$$\mathrm{a}\mathrm{car}\mathrm{drives}\mathrm{at}\mathrm{a}\mathrm{speed}\mathrm{of}120\mathrm{km}/\mathrm{hr}$$$$\mathrm{it}\mathrm{starts}\mathrm{to}\mathrm{brake}\mathrm{at}\mathrm{a}\mathrm{road}\mathrm{mark}A\mathrm{and}$$$$\mathrm{passes}\mathrm{a}\mathrm{road}\mathrm{mark}B\mathrm{at}\mathrm{a}\mathrm{speed}\mathrm{of}$$$$60\mathrm{km}/\mathrm{hr}.\mathrm{acceleration}\mathrm{is}\mathrm{constant}.\mathrm{the}$$$$\mathrm{distance}AB\mathrm{is}4\mathrm{km}.$$$$\left(1\right)\mathrm{calculate}\mathrm{the}\mathrm{acceleration}$$$$\left(2\right)\mathrm{calculate}\mathrm{the}\mathrm{time}\mathrm{between}A\mathrm{and}B$$$$\left(3\right)\mathrm{there}\mathrm{are}n\mathrm{reflector}\mathrm{posts}\mathrm{between}A$$$$\mathrm{and}B.\mathrm{calculate}\mathrm{the}\mathrm{speed}\mathrm{of}\mathrm{the}\mathrm{car}\mathrm{at}$$$$\mathrm{each}\mathrm{of}\mathrm{them}(\mathrm{find}\mathrm{a}\mathrm{function}\mathrm{for}\mathrm{the}$$$$\mathrm{speed}\mathrm{depending}\mathrm{on}\mathrm{the}\mathrm{distance}\mathrm{traveled})$$

Answered by mr W last updated on 04/Mar/20

$$v_A=120km/h$$$$v_B=60km/h$$$$\left(1\right)$$$$a=\frac{v_B^2-v_A^2}{2s}=\frac{{60}^2-{120}^2}{2\times 4}=-1350km/h^2=-\frac{5}{48}m/s^2$$$$\left(2\right)$$$$t=\frac{v_B-v_A}{a}=\frac{60-120}{-1350}=\frac{2}{45}h=160s$$$$\left(3\right)$$$$v_{\left(i\right)}=speedati-threflector$$$$\frac{v_{\left(i\right)}^2-v_A^2}{2s_{\left(i\right)}}=a$$$$v_{\left(i\right)}=\sqrt{v_A^2+2{as}_{\left(i\right)}}=v_A\sqrt{1-2\times \frac{1350}{{120}^2}\times \frac{i}{n+1}\times 4}$$$$v_{\left(i\right)}=120\sqrt{1-\frac{0.75i}{n+1}}\left(km/h\right)$$

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