(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: Quadratic & simultaneous equations

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