To solve for the force needed to accelerate the ball, we need to use the formula:
[tex]\[ F = m \cdot a \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( a \)[/tex] is the acceleration.
Given:
- The mass [tex]\( m \)[/tex] of the ball is [tex]\( 140 \)[/tex] grams,
- The acceleration [tex]\( a \)[/tex] is [tex]\( 25 \, \text{m/s}^2 \)[/tex].
First, we need to convert the mass from grams to kilograms because the standard unit of mass in the International System of Units (SI) is kilograms.
We know:
[tex]\[ 1 \, \text{kg} = 1000 \, \text{g} \][/tex]
Therefore,
[tex]\[ 140 \, \text{g} = \frac{140}{1000} \, \text{kg} = 0.14 \, \text{kg} \][/tex]
Now, we can substitute the values into the formula:
[tex]\[ F = 0.14 \, \text{kg} \cdot 25 \, \text{m/s}^2 \][/tex]
Multiplying these values:
[tex]\[ F = 3.5 \, \text{N} \][/tex]
Therefore, the force needed to accelerate the ball at [tex]\( 25 \, \text{m/s}^2 \)[/tex] is [tex]\( 3.5 \, \text{N} \)[/tex].
So, the correct answer is:
[tex]\[ \boxed{3.5 \, \text{N}} \][/tex]
