A man travelling in a car with a maximum constant speed of 20 m/s watches his friend start off at a distance of 100 m on motor cycle with constant acceleration \['a'.\] The man in the car will reach his friend when \['a'\] is | |
1. \[<2m/{{s}^{2}}\] | 2. \[>2m/{{s}^{2}}\] |
3. \[=2m/{{s}^{2}}\] | 4. \[=4m/{{s}^{2}}\] |
Which of the above option (s) is/are correct |
A) 1 and 3
B) 2 and 4
C) 1, 2 and 4
D) 4 only
Correct Answer: A
Solution :
If \[t\] is the time in which man can catch his friend. Then |
\[\left( \frac{1}{2}a{{t}^{2}}+100 \right)=20t\] Or \[\frac{a{{t}^{2}}}{2}-20t+100=0\] |
\[\therefore t=\frac{20\pm \sqrt{{{20}^{2}}-4\times a/2\times 100}}{2\times a/2}\] |
For \[t\]have real solution, |
\[{{20}^{2}}-4\times \frac{a}{2}\times 100\ge 0\] Or\[a\le 2\operatorname{m}/{{s}^{2}}\]. |
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