Why there is no work done if a particle travels with constant velocity?

Question

Definition of work is the following:

$$W = F*d$$

$F$ is the force exerted on the direction of displacement, $d$ is the distance covered.

Let's assume net acting force on an object floating in space is $0$. This object moves with a constant velocity. Let's say the speed of object is $2 \frac{m}{s}$ for any given time $t$. After $10$ seconds, we will have been covered a distance of $10*2 = 20$ meters. If we put these in the formula for work, net work done turns out $0$:

$$W = F*d=0*20 = 0$$

How this can be possible? Our object obviously has gone through a distance. It is $20$ meters away from where it started out. It has done some work.

Answer 1

Elaborating Žarko Tomičić's comment,

The work done by all the forces on a body equals the change in kinetic energy, this relation itself can be derived from F.D ( use:$\frac{v^2-u^2}{2}=a.D$ or see here)

In your question, the initial velocity is 2m/s and you are also aware that it is constant.

what is the change in its kinetic energy?

Zero, we conclude net force does no work.

Answer 2

The Newton's first law says that an object acted upon by a net zero force will continue moving with a constant veelocity (in an inertial reference frame). So there is no need for work in this case, although it does contradict to our everyday experience, where an object left to itself will eventually stop (due to various friction forces).

Let me also note that every force acting on the object produces work and this work might be non-zero even for movement with a constant velocity. It is only the net work (i.e. the some of work done by all the forces) that is zero.

Answer 3

In the work formula you are using F represents a constant force, once the net force is zero, no work is being done, the object is no longer accelerating. See; https://en.wikipedia.org/wiki/Work_(physics)#Work_and_energy

Answer 4

A zero net force does not mean zero forces nor zero work done, just the zero net force.

Scenario 1: There is no force acting on an object. The object is moving in an inertial frame by a constant velocity and no work is done.

Scenario 2: The are 2 equal but the opposite forces, like a pushing force force $\vec F$ and friction force $- \vec F$, with the zero net force. The object is moving in an inertial frame by a constant velocity as in Scenario 1, but the work done is $W = \int{\vec F \cdot \mathrm{d}\vec l}$

In the scenario 2, the pushing force does positive work, as the integral is positive. The friction force does negative work, as the integral is negative.