Answer:
2 N
Explanation:
The average power is defined as:
[tex]P=\frac{W}{\Delta t}(1)[/tex]
Here W is the work done and t is the time interval in which the work is done.
The average speed is the rate of change of the position with respect to time:
[tex]v=\frac{x}{\Delta t}\\\Delta t=\frac{x}{v}(2)[/tex]
Replacing (2) in (1):
[tex]P=\frac{Wv}{x}\\x=\frac{Wv}{P}(3)[/tex]
The work done by a force F acting on an object undergoing a distance x, is given by:
[tex]W=Fxcos\theta[/tex]
the force acts in the direction of motion of the object, so the angle between then is zero and the cosine is equal to one:
[tex]x=\frac{W}{F}(4)[/tex]
Equaling (3) and (4):
[tex]\frac{Wv}{P}=\frac{W}{F}\\F=\frac{P}{v}\\F=\frac{4W}{2\frac{m}{s}}\\F=2N[/tex]
The magnitude of the constant force acting in the direction of motion is of 2 N
Given data:
Magnitude of average power is, [tex]P_{av.} = 4 \;\rm W[/tex].
The average speed of object is, [tex]v=2 \;\rm m/s[/tex].
Let F be the constant force acting on the object. Such that the work done by the constant force is given as,
[tex]W = F \times d ...........................................(1)[/tex]
Here, d is the distance covered by the object.
The distance covered by the object is given as,
[tex]v= \dfrac{d}{t}\\d= v \times t[/tex]
Substituting the above values in equation (1) as,
[tex]W = F \times (v \times t) \\W = F \times v \times t ..........................................(2)[/tex]
Now, the average power delivered by the constant force is given as,
[tex]P_{av.} =\dfrac{W }{t}[/tex]
Substitute the value of equation (2) in above expression as,
[tex]P_{av.} =\dfrac{F \times v \times t }{t}\\P_{av.}=F \times v[/tex]
Solving as,
[tex]4=F \times 2\\F=\dfrac{4}{2}\\F=2 \;\rm N[/tex]
Thus, we can conclude that the magnitude of the constant force acting in the direction of motion is of 2 N.
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