To determine the force needed to accelerate an object, we will use Newton's second law of motion. The formula for this law is given by:
[tex]\[ F = ma \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass of the object, and
- [tex]\( a \)[/tex] is the acceleration.
Here, we are given:
- [tex]\( m = 5 \, \text{kg} \)[/tex] (the mass of the object),
- [tex]\( a = 6 \, \text{m/s}^2 \)[/tex] (the acceleration).
We substitute these values into the formula:
[tex]\[ F = 5 \, \text{kg} \times 6 \, \text{m/s}^2 \][/tex]
Carrying out the multiplication gives us:
[tex]\[ F = 30 \, \text{N} \][/tex]
Thus, the force needed to accelerate the object at [tex]\( 6 \, \text{m/s}^2 \)[/tex] is [tex]\( 30 \, \text{N} \)[/tex].
The correct answer is:
[tex]\[ \boxed{30 \, \text{N}} \][/tex]
