# 2 football players who are 20m apart run towards each other. Player 1 runs at 6m/s, his acceleration is 0. Player 2 starts from rest and he accelerates at 4.0m/s When do they collide?

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We can solve this problem using a kinematic equation.

Let `d_1` = distance travelled by player 1

Let `d_2` = distance travelled by player 2

`d_1=v_(i1)t+0.5a_1t^2`

`=6t`

`d_2 = v_(i2)t+0.5a_2t^2`

`=2t^2`

When the two meet, they will have together travelled 20m:

`d_1+d_2=20`

`6t+2t^2=20`

`t^2+3t-10=0`

Using factoring:

`(t+5)(t-2)=0`

Therefore, t=-5 and t=2

Since time cannot be negative, they will meet after they have run for 2 seconds at which point:

`d_1=6(2)=12`

`d_2=2(2)^2=8`

Player 1 will have run 12m and player 2 will have run 8m.

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