Question

Question #2cf14

Answer 1

`61.1` meters

Explanation:

To find the distance it takes to come to a complete stop, we need to use the formula relating velocity, acceleration, and position:

`v_f^2 = v_i^2 + 2aDeltax`

We know our `v_i` is 17.9 meters per second, and our `v_f` is 0.0 meters per second. However, the problem doesn't directly tell us the acceleration or the distance traveled (`Deltax`).

We can find the acceleration by using this formula:

`a = (Deltav)/(Deltat) = (v_f - v_i)/(Deltat) = (0.0 - 17.9" m/s")/(6.83 " s") = (-17.9)/(6.83) "m"/"s"^2 = -2.62 "m"/"s"^2`

Now that we have our acceleration, we can plug it in to the first equation and solve for `Deltax`.

`v_f^2 = v_i^2 + 2aDeltax`

`(0.0 "m"/"s")^2 = (17.9 "m"/"s")^2 + 2(-2.62 "m"/"s"^2)(Deltax)`

`0.0 "m"^2/"s"^2 = 320. "m"^2/"s"^2 - 5.24 "m"/"s"^2 * (Deltax)`

`-320. "m"^2/"s"^2 = -5.24 "m"/"s"^2 * (Deltax)`

`61.1 "m" = Deltax`

So Maggie will need to apply her brakes `61.1` meters before the stop sign in order to come to a complete stop.

Final Answer