Help with physics"(?)"

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1 Answer
May 14, 2018

Assuming that the bus driver is kind, the bus driver will see the boy at t = 8" s", begin to stop, and allow the boy to enter the bus.

Explanation:

"A bus begins to move with an acceleration of 1" m/s"^2" gives the following equation:

x_"bus"(t) = 1/2(1" m/s"^2)t^2" [1]"

"A boy 48" m" behind the bus starts running at 10" m/s"" gives us the following equation:

x_"boy"(t) = (10" m/s")t-48" m [2]"

We want the time, t, when x_"bus"(t) = x_"boy"(t), therefore, we set the right of equation [1] equal to the right side of equation [2]:

1/2(1" m/s"^2)t^2 = (10" m/s")t-48" m"

Divide both sides by 1/2(1" m/s"^2)

t^2 = (20" s")t-96" s"^2

Rewrite so that the equation is 0:

t^2 - (20" s")t+96" s"^2=0

Factor:

(t -8" s")(t-12" s")

t = 8" s" and t = " 12" s"