Help with physics"(?)"

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Help with physics"(?)"

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Answer 1 · 2018-05-14T03:05:37

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

Explanation:

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

$x_{bus} (t) = \frac{1}{2} (1 {m/s}^{2}) t^{2} [1]$ $x_"bus"(t) = 1/2(1" m/s"^2)t^2" [1]"$

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

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

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

$\frac{1}{2} (1 {m/s}^{2}) t^{2} = (10 m/s) t - 48 m$ $1/2(1" m/s"^2)t^2 = (10" m/s")t-48" m"$

Divide both sides by $\frac{1}{2} (1 {m/s}^{2})$ $1/2(1" m/s"^2)$

$t^{2} = (20 s) t - 96 s^{2}$ $t^2 = (20" s")t-96" s"^2$

Rewrite so that the equation is 0:

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

Factor:

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

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

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