Answer:
We know that:
Distance between Odysseus and Penelope = 50m
Speed of Odysseus = So = 4m/s
Speed of Penelope = Sp = 6m/s.
Now we want to find the equation of motion for Odysseus.
First, let's find the amount of time that he is moving, we know that when he meets with Penelope, he will stop moving.
Now they weel meet each other when the total distance traveled by both of them is equal to 50m.
Then, recalling that:
Distance = Time*speed.
50m = 4m/s*t + 6m/s*t = 10m/s*t
t = 50m/10m/s = 5s
They will move for 5 seconds.
Now we can write the movement equation for Odysseus as:
p(t) = 4m/s*t + p0 for (0s ≤ t ≤ 5s)
Where p0 is the initial position of Odysseus, and because we can put our coordinate axis where we want, we can define p0 = 0m.
Then the position of Odysseus is:
P(t) = 4m/s*t if 0s ≤ t ≤ 5s
P(t) = 4m/s*5s = 20m if t > 5s.
The second piece says that for t larger than 5 seconds, he will not move (at least for a given amount of time)
