Answer:
Approximately [tex]2.3\; {\rm s}[/tex].
Explanation:
Acceleration is the rate of change in velocity. When acceleration is constant, dividing the change in velocity by acceleration would give the duration of the motion.
To find the change in velocity, subtract initial velocity from the current velocity:
[tex]\begin{aligned} & (\text{change in velocity}) \\=\; & (\text{current velocity}) - (\text{initial velocity}) \\ =\; & 0\; {\rm m\cdot s^{-1}} - 8.8\; {\rm m\cdot s^{-1}} \\ =\; & (-8.8)\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].
(Negative because velocity is decreasing.)
It is given that the bus is decelerating at [tex]3.9\; {\rm m\cdot s^{-2}}[/tex], meaning that the acceleration would be [tex](-3.9)\; {\rm m\cdot s^{-2}}[/tex] (again, negative because velocity is decreasing.)
Divide the change in velocity by acceleration to find the duration of the motion:
[tex]\begin{aligned}(\text{duration}) &= \frac{(\text{change in velocity})}{(\text{acceleration})} \\ &= \frac{(-8.8)\; {\rm m\cdot s^{-1}}}{(-3.9)\; {\rm m\cdot s^{-2}}} \\ &\approx 2.3\; {\rm s}\end{aligned}[/tex].
In other words, the bus would stop in approximately [tex]2.3\; {\rm s}[/tex].
