Sure, I'll walk you through the solution step-by-step for this problem.
1. Understand the problem:
- We need to calculate the force required to accelerate a ball with a mass of 140 grams at a rate of [tex]\(25 \, \text{m/s}^2\)[/tex].
- The formula for force is [tex]\( F = ma \)[/tex], where [tex]\( F \)[/tex] is the force, [tex]\( m \)[/tex] is the mass, and [tex]\( a \)[/tex] is the acceleration.
2. Convert the mass to kilograms:
- The mass is given in grams, but the standard unit for mass in physics (when using SI units) is kilograms.
- To convert from grams to kilograms, we divide by 1000.
[tex]\[
m = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg}
\][/tex]
3. Plug the values into the formula:
- We have the mass [tex]\( m = 0.14 \, \text{kg} \)[/tex] and the acceleration [tex]\( a = 25 \, \text{m/s}^2 \)[/tex].
- Using the formula [tex]\( F = ma \)[/tex]:
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2
\][/tex]
- Perform the multiplication:
[tex]\[
F = 3.5 \, \text{N}
\][/tex]
4. Compare with the given options:
- The options provided are: 3.5 N, 115 N, 165 N, and 4.5 N.
- From our calculation, the force required is 3.5 N.
Therefore, the correct answer is [tex]\( \boxed{3.5 \, \text{N}} \)[/tex].
