As the shuttle bus comes to a sudden stop to avoid hitting a dog, it accelerates uniformly at -4.1 m/s as it slows from 9.0m/s to 0m/s. What is the time needed for the bus stop?

v = at, so t = v/a = (-9.0 m/s) / (-4.1 m/s^2) = 2.195 s

This simple version works only because the bus came to a complete stop.

To find the time needed for the bus to stop, we can use the equation of motion:

v = u + at

Where:
v = final velocity (0 m/s)
u = initial velocity (9.0 m/s)
a = acceleration (-4.1 m/s^2)
t = time

First, let's rearrange the equation to solve for t:

t = (v - u) / a

Substituting the given values:

t = (0 - 9.0) / -4.1

Next, we can calculate the time:

t = (-9.0) / -4.1
t ≈ 2.1951 seconds

Therefore, the time needed for the bus to stop is approximately 2.1951 seconds.

To find the time needed for the bus to stop, we can use the equation of motion that relates the final velocity (v), initial velocity (u), acceleration (a), and time (t):

v = u + at

In this case, the initial velocity (u) is 9.0 m/s, the final velocity (v) is 0 m/s, and the acceleration (a) is -4.1 m/s² (negative because it's slowing down in the opposite direction). We need to find the time (t).

Let's rearrange the equation to solve for time:

v = u + at
0 = 9.0 + (-4.1)t
-9.0 = -4.1t

Now, let's isolate the variable t:

-4.1t = -9.0

Divide both sides of the equation by -4.1:

t = -9.0 / -4.1

Simplifying the right side of the equation:

t ≈ 2.195122

Therefore, the time needed for the bus to stop is approximately 2.195 seconds.