Answer:
The time taken to stop the box equals 1.33 seconds.
Explanation:
Since frictional force always acts opposite to the motion of the box we can find the acceleration that the force produces using newton's second law of motion as shown below:
[tex]F=mass\times acceleration\\\\\therefore acceleration=\frac{Force}{mass}[/tex]
Given mass of box = 5.0 kg
Frictional force = 30 N
thus
[tex]acceleration=\frac{30}{5}=6m/s^{2}[/tex]
Now to find the time that the box requires to stop can be calculated by first equation of kinematics
The box will stop when it's final velocity becomes zero
[tex]v=u+at\\\\0=8-6\times t\\\\\therefore t=\frac{8}{6}=4/3seconds[/tex]
Here acceleration is taken as negative since it opposes the motion of the box since frictional force always opposes motion.
