Problema Solution
Suki is training in her wheelchair for the 100-meter race at the next Paralympics. In her initial acceleration phase she averages a speed of 2.7 meters per second. At her maximum speed phase she averages a speed of 6.6 meters per second. If she finishes a practice race in 18.1 seconds, how many meters long (to the nearest 10th of a meter) is her initial acceleration phase?
Answer provided by our tutors
let
d = 100 m
v1 = 2.7 mps
t1 = the time of the race passed with speed v1
v2 = 6.6 mps
t2 = the time of the race passed with speed v2
t = 18.1 s
t1 + t2 = 18.1
since speed = distance/time => distance = speed*time
v1*t1 + v2*t2 = d
2.7t1 + 6.6t2 = 100
by solving the system of equations
t1 + t2 = 18.1
2.7t1 + 6.6t2 = 100
we find
t1 = 973/195 s
t2 = 5113/390 s
click here to see the step by step solution of the system of equations
the length of the initial acceleration phase is
v1*t1 = 2.7*(973/195) = 13.5 m