Question

During a certain time interval, a constant force delivers an average power of 4 watts to an object. if the object has an average speed of 2 meters per second and the force acts in the direction of motion of the object, what is the magnitude of the force f~ ?

Answer 1

Force = Work done / distance = 4Nm / 2m = 2N

Answer 2

Answer:

2 N

Explanation:

The average power is defined as:

$P=\frac{W}{\Delta t}(1)$

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:

$v=\frac{x}{\Delta t}\\\Delta t=\frac{x}{v}(2)$

Replacing (2) in (1):

$P=\frac{Wv}{x}\\x=\frac{Wv}{P}(3)$

The work done by a force F acting on an object undergoing a distance x, is given by:

$W=Fxcos\theta$

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:

$x=\frac{W}{F}(4)$

Equaling (3) and (4):

$\frac{Wv}{P}=\frac{W}{F}\\F=\frac{P}{v}\\F=\frac{4W}{2\frac{m}{s}}\\F=2N$