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"#