Question

Two trains one of length 100 m and another of 125 m are moving in mutially opposite directions along the parallel lines , meet each other , each with a speed 10 m/s . If their accelerations are 0.3 m/s² and 0.2m/s² respectively , then at what time will they take to pass each other?

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{Relative}\mathrm{velocity}\mathrm{of}\mathrm{one}\mathrm{train}\mathrm{w}.\mathrm{r}.\mathrm{t}.\mathrm{other}=10+10=20\mathrm{m}/\mathrm{s} \\ \mathrm{Relative}\mathrm{acceleration}=0.3+0.2=0.5\mathrm{m}/{\mathrm{s}}^2 \\ \mathrm{If}\mathrm{train}\mathrm{cross}\mathrm{each}\mathrm{other}\mathrm{then}\mathrm{from}\mathrm{second}\mathrm{equation}\mathrm{of}\mathrm{motion}, \\ \mathrm{s}=\mathrm{ut}+\frac{1}{2}{\mathrm{at}}^2 \\ \mathrm{As},\mathrm{s}={\mathrm{s}}_1+{\mathrm{s}}_2 \\ \Rightarrow \mathrm{s}=100+125=225\mathrm{m} \\ 225=20\mathrm{t}+\frac{1}{2}\times 0.5\times {\mathrm{t}}^2 \\ 0.5{\mathrm{t}}^2+40\mathrm{t}-450=0 \\ \mathrm{t}=\frac{-40\pm \sqrt{{\left(40\right)}^2-4\times 0.5\times \left(-450\right)}}{2\times 0.5} \\ \mathrm{t}=\frac{-40\pm \sqrt{1600+900}}{1} \\ \mathrm{t}=-40\pm \sqrt{2500} \\ \mathrm{t}=-40\pm 50 \\ \mathrm{t}=-40+50\mathrm{or}\mathrm{t}=-40-50 \\ \mathrm{t}=10\mathrm{or}\mathrm{t}=-90 \\ \mathrm{We}\mathrm{know}\mathrm{that}\mathrm{time}\mathrm{cannot}\mathrm{be}\mathrm{negative}. \\ \mathrm{Hence},\mathrm{t}=10\mathrm{s} \end{gathered}$$