Réponse:
72 J
Explications:
First, let's calculate the variation in the body's momentum (\( \Delta p \)):
\[ F = \frac{\Delta p}{\Delta t} \]
\[ \Delta p = F \cdot \Delta t \]
\\Delta p = 12 \, \text{N} \times 2 \, \text{s} \]
\[ \Delta p = 24 \, \text{kg} \, \text{m/s} \]
Now we can find the velocity (\( v \)) of the body using the definition of momentum:
\p = m \cdot v \]
\[ v = \frac{\Delta p}{m} \]
\[ v = \frac{24 \, \text{kg}}, \text{m/s}{4 \, \text{kg}} \]
\[ v = 6, \text{m/s} \]
Now that we have the speed (v) of the body, we can calculate the kinetic energy (E_c):
\E_c = \frac{1}{2} m v^2 \]
\[ E_c = \frac{1}{2} \times 4 \, \text{kg} \times (6 \, \text{m/s})^2 \]
\E_c = \frac{1}{2} \times 4 \, \text{kg} \times 36 \\, \text{m}^2/\text{s}^2 \]
\[ E_c = 72 \, \text{J} \]
So the kinetic energy gained by the body is 72 joules.
