Calculating Work Done: Force and Displacement

Given Information

The problem involves calculating the work done on a body. The following values are provided:

• Force ($F$) = 5 N
• Displacement ($d$) = 50 m
• Direction: The force and displacement are in the same direction.

Work Done Formula

The work done ($W$) by a constant force ($F$) causing a displacement ($d$) is given by the formula:

$W = F \times d \times \cos(\theta)$

where $\theta$ is the angle between the force vector and the displacement vector.

Calculation

Since the force and displacement are in the same direction, the angle $\theta$ between them is $0^\circ$. The cosine of $0^\circ$ is 1:

$\theta = 0^\circ$

$\cos(0^\circ) = 1$

Now, substitute the given values into the work done formula:

$W = (5 \, \text{N}) \times (50 \, \text{m}) \times 1$

$W = 250 \, \text{N} \cdot \text{m}$

The unit N$\cdot$m is equivalent to Joules (J). Therefore:

$W = 250 \, \text{J}$

The work done is positive because the force acts in the direction of displacement.

Final Answer

The work done under the action of this force is +250 J.