Two soccer players start from rest, 36 m apart. they run directly toward each other, both players accelerating. the first player’s acceleration has a magnitude of 0.58 m/s2. the second player’s acceleration has a magnitude of 0.42 m/s2. (a) how much time passes before the players collide? (b) at the instant they collide, how far has the first player run?

A) Both players are moving by uniformly accelerated motion, and we can write the position at time t of each of the two players as follows:


where
is the acceleration of the first player
is the acceleration of the second player
is the initial distance between the two players
and where I put a negative sign in front of the acceleration of the second player, since he's moving in the opposite direction of the first player.

The time t at which the two players collide is the time t at which , therefore:

from whic we find


b) We can use the equation of  to find how far the first player run in t=8.5 s:

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