Sam the Speeder is driving at a constant speed of 30 m/s, which is over the spee

Question

Sam the Speeder is driving at a constant speed of 30 m/s, which is over the speed limit. Corey the Cop sees Sam when he is 15 m away, coming towards him. Corey sets out to catch him, accelerating from rest at a constant rate of 15 m/s2 in the same direction as Sam's motion.

Sam and Corey will actually be in the same location twice-- the first time when Corey is going slow and Sam blows by, and the second when Corey has had a chance to catch up to Sam again. What are these two times?

first time:
second time:

Explanation / Answer

Dist covereed by Sam = 15 + Dist covered by cop

15*t = 15 + u*t + 0.5*a*t^2

15t = 15 + 0 +0.5*30*t^2

15t^2 -15t +15 = 0

On solving the above eq., we get:

t1 = 1s , t2 = 1s

we have identical roots. This means Sam and Corey will actually be in the same location at t = 1s with same speed.

first time: 1s
second time: 1s

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