;; Complete the following functions

;; compute constant acceleration
;; a = (2s) / (t^2)
(define (const-accel s t)
  (/ (* s 2) (* t t)))

;; find Usain's acceleration (100m)
(define usain-accel-100 (const-accel 100 time-100))

;; find Usain's final speed (100m)
(define usain-v-final-100
  (* time-100 usain-accel-100))

(define (square x) (* x x))

;; find amount of for Usain to reach max speed (200m)
(define usain-t-v-max-200
  (- time-200
     (sqrt(-
           (square time-200)
           (/ 400 usain-accel-100)))))

;; find Usain's max speed (200m)
(define usain-v-max-200
  (* usain-accel-100 usain-t-v-max-200))

;; find Usain's time (second 100m)
(define usain-t-2nd-100-of-200
 (if (<= (* 0.5 usain-accel-100 (square usain-t-v-max-200) ) 100)
     (/ 100 usain-v-max-200)
     (- time-200 (sqrt (/ 200 usain-accel-100)))))