Answer:
[tex]\boxed {\boxed {\sf 3.75 \ seconds }}[/tex]
Explanation:
Average acceleration is found by dividing the change in acceleration by the time.
[tex]a=\frac{ v_f-v_i}{t}[/tex]
The shuttle bus has an acceleration of -2.4 meters per square second. It slows from 9.0 meters per second to rest, or 0 meters per second. Therefore:
[tex]a= -2.4 \ m/s^2 \\v_f= 0 \ m/s \\v_i= 9 \ m/s[/tex]
Substitute the values into the formula.
[tex]-2.4 \ m/s^2=\frac{0 \ m/s - 9 \ m/s}{t }[/tex]
Solve the numerator.
[tex]-2.4 \ m/s^2 = \frac{-9 \ m/s}{t}[/tex]
We want to solve for t, the time. We have to isolate the variable. Let's cross multiply.
[tex]\frac{-2.4 \ m/s^2}{1} = \frac{-9 \ m/s}{t}[/tex]
[tex]-9 \ m/s *1= -2.4 \ m/s^2 *t[/tex]
[tex]-9 \ m/s=-2.4 m/s^2*t[/tex]
t is being multiplied by -2.4. The inverse of multiplication is division, so divide both sides by -2.4
[tex]\frac{-9 \ m/s }{-2.4 \ m/s^2} =\frac{ -2.4 \ m/s^2*t}{-2.4 \ m/s^2}[/tex]
[tex]\frac{-9 \ m/s }{-2.4 \ m/s^2} =t[/tex]
[tex]3.75 \ s=t[/tex]
It takes 3.75 seconds.
