Question

A runner wants to run 10,000m in 30 minutes. After 27 minutes he has run 8,900m. For how long must he accelerates at 0.02 m/s² and then maintain that final speed?

Answer 1

$$t_{max}=(30-27)60=180\ s\\v=\frac{8900}{27\cdot60}=5.49\frac{m}{s}$$

$$10000=8900+5.49t+0.5(0.02)t^2\\t=156\ s$$