The movement of two motorcyclists is given by the equations x1 = 15 + t2 and x2 = 8t.

The movement of two motorcyclists is given by the equations x1 = 15 + t2 and x2 = 8t. Describe the movement of each motorcyclist; find the place and time of their meeting.

First motorcyclist: initial coordinate 15m, uniformly accelerated movement, a = 2m / s.
Second motorcyclist: initial coordinate 0m, uniform movement, V = 8m / s
The place of their meeting is designated x3 and x4. Then:
15 + t ^ 2 = x3 = 8t
15 + t ^ 2 = 8t
t ^ 2-8t + 15 = 0
D = 64-60 = 4
t1 = (8-2) / 2 = 3c
t2 = 5c
This means that they will meet twice, the first time: the first motorcyclist did not accelerate, the second overtook him; second time: the first motorcyclist eventually accelerated and caught up with the second.
Find the coordinates:
x3 = 15 + t1 ^ 2 = 15 + 9 = 24m
x4 = 15 + t2 ^ 2 = 15 + 25 = 40m