## Statement

difficulty

A 6kg body initially on repose experiences a force of 10 N for 4 seconds. What distance does it travel?

## Solution

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:

$\stackrel{\to }{F}=m·\stackrel{\to }{a}⇒F=m·a⇒10=6·a⇒a=\frac{10}{6}m/{s}^{2}$

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:

Thus, the body traverses 13.3 m in 4 seconds.

## Formulas worksheet

These are the main formulas that you must know to solve this exercise. If you are not clear about their meaning, we recommend you to check the theory in the corresponding sections. Furthermore, you will find in them, under the Formulas tab, the codes that will allow you to integrate these equations in external programs like Word or Mathematica.

Formulas
Related sections
$F=m·a$
$x={x}_{0}+{v}_{0}t+\frac{1}{2}a{t}^{2}$