1. The problem statement, all variables and given/known data A sprinter accelerates from rest to a top speed with an acceleration which magnitude is 3.80 m/s^2 . After achieving top speed, he runs the remainder of the race without speeding up or slowing down. The total race is 50 m long. If the total race is run in 7.88 s, how far does he run during the acceleration phase? 2. Relevant equations By using equations of motion the following 2 equations arise: s= ut +1/2at^2 = 1/2(3.8)t^2 = 1.9t^2 .......... (1) From v= u+at and v= s'/t' : s= -3.8t(7.88-t)+50...........(2) 3. The attempt at a solution The two simultaneous equations lead to : 0= 1.9 ^2-29.94t+50, a quadrqtic equation, which is solved: s= 6.85 m Can someone please show me step-by-step how they arrived at the final solution. The part that puzzles me the most is how they derived the second equation. Any input is kindly welcomed. Thank you all.