A) \[8\text{ }m{{s}^{-1}}\]
B) \[5\text{ }m{{s}^{-1}}\]
C) \[12\text{ }m{{s}^{-1}}\]
D) \[10\text{ }m{{s}^{-1}}\]
Correct Answer: D
Solution :
The student is able to catch the bus if in time t the distance travelled by him is equal to the distance travelled by bus in time t i.e. \[{{s}_{1}}={{s}_{2}}\] ... (i) From eq. (1) \[0+\frac{1}{2}a{{t}^{2}}=ut-d\] or \[{{t}^{2}}-2ut+2d=0\] It is quadratic equation So, \[t=\frac{-2\pm \sqrt{4{{u}^{2}}-8ad}}{2}\] \[=\frac{-2\pm 2\sqrt{{{\mu }^{2}}-2ad)}}{2}\] For t to be real \[u\ge \sqrt{2ad}\ge \sqrt{2\times 1\times 50}=10\,m/s\] \[=10\,\,m{{s}^{-1}}\]
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