Calculate the acceleration.

Acceleration is the change in velocity over time.

$$a = \frac{v - u}{t}$$

Given:
Initial speed $u = 10\, \text{m/s}$
Final speed $v = 30\, \text{m/s}$
Time $t = 5\, \text{s}$

Substitute the values:

$$a = \frac{30\, \text{m/s} - 10\, \text{m/s}}{5\, \text{s}}$$ $$a = \frac{20\, \text{m/s}}{5\, \text{s}}$$ $$a = 4\, \text{m/s}^2$$

According to Newton's second law, force is the product of mass and acceleration.

$$F = ma$$

Given:
Mass $m = 3\, \text{kg}$
Acceleration $a = 4\, \text{m/s}^2$

Substitute the values:

$$F = 3\, \text{kg} \times 4\, \text{m/s}^2$$ $$F = 12\, \text{N}$$

The magnitude of the force is $\text{12 N}$.