What is Donald's distance from the starting line 7 + z seconds after the race started?

Question

When running a 100 meter race Donald reaches his maximum speed 7 seconds after the race started when he is 35 meters from the starting line. Donald runs at this max speed for the rest of the race. Donald is 63 meters from the starting line 11 seconds after the start of the race.

Answer 1

After 7 seconds Donald is 35 meters plus whatever distance he runs during those additional seconds. Let's call his maximum velocity "v".

So we can write an equation for the distance as d = 35 + v•t

Since we know that at t = 11 his distance is 63 meters, then 63 = 35 + v•7 and we can now solve for "v":

63 = 35 + v•7

28 = 7v

v = 4 m/s

So now we can plug that back into our equation d = 35 + v•t to get:

d = 35 + 4t

So at time t = 7 + z we get:

d = 35 + 4(7 + z)

d = 35 + 28 + 4z

d = 63 + 4z