I'm confused on the 6+z question and the x seconds question

Question

When running a 100-meter race Jeremy reaches his maximum speed 6 seconds after the race started when he is 40 meters from the starting line. Jeremy runs at this max speed for the rest of the race. Jeremy is 75 meters from the starting line 11 seconds after the start of the race.

What is Jeremy's distance from the starting line 6+z seconds after the race started?

What is Jeremy's distance from the starting line x seconds after the race started (provided x≥6)?

Answer 1

Let 1 the end of the constant acceleration interval and 2, the const velocity interval from 1 to the 75 m mark

t₁ = 6 d₁= 1/2 at₁² = 18a and v₁ = at₁ = 6a

t₂=t_T-t₁ = 11-6 = 5 s v₂ = v₁ = 6a d₂ = 75 - d1 = 75 - 18a but also d₂ = v₂t₂ = 6a(5) = 30a

We can solve for a: 75-18a = 30a a = 75/48 = 25/16 = 1.5625

We now know all the variables at 1 and 2 and total.

a) d(6+z) = d₁ + zv₂

b) d(x) = d₁ + (x-6)v₂ ( for x>6 )

You can substitute in numbers for d₁ and v₂

Please consider a tutor. Take care