When running a 100 meter race Trevor reaches his maximum speed when he is 40 meters from the starting line, and 6 seconds have elapsed since the start of the race. Trevor continues at this max speed for the rest of the race and is 72 meters from the starting line 10 seconds after the start of the race.

a. What is Trevor's max speed?

b. Suppose Trevor runs for an additional 3 seconds after reaching his max speed ...

-How far will Trevor travel during those additional 3 seconds?

-What is Trevor's distance from the starting line 9 seconds after the race started?

c. What is Trevor's distance from the starting line 7.5 seconds after the race started?

a) The max speed is 8 m/s

b1) Trevor will travel 24 m in 3 s after reaching max speed.

b2) After 9 s of starting the race, Trevor will run 64 m

Explanation:

For a straight movement with constant speed (as Trevor running after 6 s) the variation of the position over time (dx / dt) is constant (v):

dx / dt = v

separating variables:

dx = v dt

Integrating both sides of the equation, the left side between the position at time "t" (x) and the initial position (x0), and the right side between time "t" and the initial time (t = 0):

x - x0 = v t

x = vt + x0

a) We know that Trevor runs 72 m in 10 s after starting the race, 6 s at variable speed and 4 s at constant max speed. We can use the equation of position to obtain this max speed:

x = vt + x0

Since Trevor starts running at constant speed after 40 m, the initial position will be 40 m. The time will be 4 s because that is the time that Trevor runs at constant speed. Then:

72 m = v * 4 s + 40 m

v = 8 m/s

b1) Knowing the max speed, we can calculate how far Trevor will run during 3s after reaching the max speed:

x = vt = 8 m/s * 3s = 24 m

b2) During the first 6 s Trevor runs 40 m and 3 s after reaching 40 m Trevor runs 24 m more. The Trevor's distance from the starting line after 9 s will be

40 m + 24 m = 64 m