Certainly! Let's solve the problem of calculating the force required to produce an acceleration of [tex]\( 5 \, \text{m/s}^2 \)[/tex] on a body with a mass of [tex]\( 6 \, \text{kg} \)[/tex].
To find the force, we can use Newton's second law of motion. Newton's second law states that the force acting on an object is equal to the mass of that object multiplied by its acceleration. The formula is written as:
[tex]\[ F = m \times a \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass, and
- [tex]\( a \)[/tex] is the acceleration.
Given data:
- Mass ([tex]\( m \)[/tex]) = [tex]\( 6 \, \text{kg} \)[/tex]
- Acceleration ([tex]\( a \)[/tex]) = [tex]\( 5 \, \text{m/s}^2 \)[/tex]
Step-by-step solution:
1. Identify the mass of the body ([tex]\( m \)[/tex]): [tex]\( 6 \, \text{kg} \)[/tex].
2. Identify the acceleration ([tex]\( a \)[/tex]): [tex]\( 5 \, \text{m/s}^2 \)[/tex].
3. Substitute the given values into the formula [tex]\( F = m \times a \)[/tex]:
[tex]\[ F = 6 \, \text{kg} \times 5 \, \text{m/s}^2 \][/tex]
4. Perform the multiplication:
[tex]\[ F = 30 \, \text{N} \][/tex]
Therefore, the force required to produce an acceleration of [tex]\( 5 \, \text{m/s}^2 \)[/tex] on a body with a mass of [tex]\( 6 \, \text{kg} \)[/tex] is [tex]\( 30 \, \text{N} \)[/tex].
