Traveled distance by a body from force

Data

• Mass of the body m = 6 kg
• Force the body is subdued F = 10 N
• Time during the force acts t = 4 s

Previous considerations

We can suppose all the forces, accelerations and motion occurs at the axis x, so we can solve the problem from the values of those magnitudes.

Resolution

Firstly, we know when a force acts on a body, an acceleration of the same direction as the force appears. If we assume the mass remains constant all the time, we can say:

$$\overrightarrow{F}=m·\overrightarrow{a}\Rightarrow F=m·a\Rightarrow 10=6·a\Rightarrow a=\frac{10}{6}m/s^2$$

Obtaining the acceleration produced by a force, the problem is reduced to a kinematics with an uniformly accelerated rectilinear movement. Remember that:

$$x=x_0+v_{0}t+\frac{1}{2}a{t}^2$$

Having into account the body starts at repose ( v₀=0 ), we can replace:

$$x=\cancel{x_0+v_{0}t}+\frac{1}{2}·a·t^2=\frac{1}{2}·\frac{10}{6}·4^2=13.3 m$$

Thus, the body traverses 13.3 m in 4 seconds.