question_answer

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\[a\le 2\operatorname{m}/{{s}^{2}}\].