Question

Help with physics"(?)"

Answer 1

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"`