when the shuttle bus come to a sudden stop to avoid hitting a dog, it decelerates uniformly at 4.6 m/s^2 as is slows from 8.2 m/s to 0 m/s. How long does it take for the acceleration for the bus. Answer in units of s

a = (Vf-Vo) / t = -4.6m/s^2,

(0-8.2) / t = -4.6,
-8.2 / t = -4.6,
t = -8.2 / -4.6 = 1.78s.

To find the time it takes for the bus to decelerate, we can use the equation of motion:

v = u + at

Where:
v = final velocity (0 m/s, as the bus comes to a stop)
u = initial velocity (8.2 m/s)
a = acceleration (-4.6 m/s², as it is decelerating)
t = time

Rearranging the equation to solve for t, we have:

t = (v - u) / a

Substituting the values:

t = (0 - 8.2) / (-4.6)

Now, let's calculate the value:

t = -8.2 / -4.6 = 1.78 seconds (rounded to two decimal places)

Therefore, the time it takes for the bus to decelerate is approximately 1.78 seconds.