1) The magnitude of the force is 4.37 N
2) The distance covered is 17.0 m
Explanation:
1)
In order to find the force needed to bring the mass at rest, we need to find its acceleration first.
The acceleration is given by:
[tex]a=\frac{v-u}{t}[/tex]
where
u = 4.00 m/s is the initial velocity of the mass
v = 0 is its final velocity
t = 8.47 is the time interval
Solving the equation,
[tex]a=\frac{0-4.00}{8.47}=-0.47 m/s^2[/tex]
Now we can find the net force acting on the mass, which is given by Newton's second law:
[tex]F=ma[/tex]
where
m = 9.30 kg is the mass
[tex]a=-0.47 m/s^2[/tex] is the acceleration
Substituting,
[tex]F=(9.30)(-0.47)=-4.37 N[/tex]
So, the magnitude of the force is 4.37 N.
2)
The distance through which the mass has moved can be found by using the following suvat equation:
[tex]s=ut+\frac{1}{2}at^2[/tex]
where
u = 4.00 m/s is the initial velocity
t = 8.47 s is the time
[tex]a=-0.47 m/s^2[/tex] is the acceleration
s is the distance covered
Solving for s,
[tex]s=(4.00)(8.47)+\frac{1}{2}(-0.47)(8.47)^2=17.0 m[/tex]
Learn more about acceleration, forces and Newton's laws of motion:
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