# Question #6e96b

Aug 1, 2015

$v = 8 \sqrt{5} \text{m/s}$

#### Explanation:

Just after bus started
For bus: Displacement, $x = \left(\frac{1}{2}\right)$ x $\left(0.2\right)$${t}^{2}$
For man: Displacement, $80 + x = v t$

To get close to the bus:

$0.1 \cdot {t}^{2} = v t - 80$ ; eliminating $x$ from above two equations

=> ${t}^{2} - 10 v t + 800 = 0$

To get the real solution of the above quadratic equation;

$10 {v}^{2} - 4 \cdot 1 \cdot 80 \ge 0$

This means that

${v}^{2} \ge 320$

so, the minimum speed will be

$\sqrt{{v}^{2}} = \sqrt{320} \implies v = 8 \sqrt{5} \text{m/s}$