No, it is not possible for a body to be in accelerated motion under the influence of a force without any work being done by the force. According to the work-energy theorem, the net work done on a body is equal to its change in kinetic energy. If the net work done on a body is zero, then its kinetic energy remains constant, which means that the body cannot accelerate.

Mathematically, the work-energy theorem is expressed as:

```

W = ΔK

```

where:

* W is the net work done on the body

* ΔK is the change in the body's kinetic energy

If W = 0, then ΔK = 0, which means that the body's kinetic energy does not change. Therefore, the body cannot accelerate.

In other words, for a body to accelerate, there must be a net force acting on it, and this force must do positive work on the body. If the net work done on the body is zero, then the body cannot accelerate.