Can someone please tell me if I've approached this homework problem correctly. A boy is running at his best speed of 6.0 m/s to catch a bus stopped at the lights. When he is 16 m from the bus, the light goes green and the bus pulls away at an acceleration of 1.0 m/s/s. Does he catch up with the bus and if yes how far does he have to run?

Question

I set the distance of the boy equal to the distance of the bus in order for him to catch up to it and got: 6t=16 +1/2t^2, then solved the quad. equation to get t=4 or 8. So he ran 24m till he caught the bus. Did I do this correctly.

Answer 1

That is the right equation. I will rewrite it as:

t^2 -12t + 32 = 0
(t-4)(t-8) = 0
(The t=8 time is when the bus would pull past him, if he didn't get on and passed it at t=4)

He will have run 24 s at t=4. Yes, you did it right. Nice job.

Answer 2

Yeah! thank you very much for checking my work. I can go to bed now.

Answer 3

I meant 24 meters, not 24 seconds. You figured that out already