Answer
Distance covered by me before I catch the bus = 74.138m
My speed at that moment = 11.93m/s
No an average college student will not be able to catch, World record of Usain Bolt is that of 10.44 m/s
Average man runs with speed of 6-8m/s
Work Step by Step
Let us first calculate the time taken to catch the bus
I have cover distance of 12m plus whatever distance the bus moves subsequently after I start running.
So,
Distance moved by bus in time t = $5t$
Distance covered by me in time t = $\frac{1}{2}at^{2} = \frac{1}{2}(0.96)t^{2}$
To catch the bus, $12+5t = \frac{1}{2}(0.96)t^{2}$
Solving the quadratic equation gives
$t = 12.428, -2.011$
Time can not be negative so -2.011 sec neglected
So distance covered before bus is caught =
$\frac{1}{2}(0.96)(12.428)^{2} = 74.138 m$
My speed at that moment would be $v = at = 0.96*12.428 = 11.93m/s$
No an average college student will not be able to achieve this.
World record of fastest speed by Usain Bolt is of 10.44m/s
