Answer :
Sure, let's break down the solution step-by-step:
1. Determine the mass in kilograms:
The mass of the ball is given in grams (140 g). We need to convert this mass to kilograms because the standard unit of mass in physics calculations is kilograms (kg).
- Conversion factor: [tex]\( 1 \text{ kg} = 1000 \text{ g} \)[/tex]
- Therefore, [tex]\(140 \text{ g} = \frac{140}{1000} \text{ kg} = 0.14 \text{ kg}\)[/tex]
2. Identify the acceleration:
The acceleration is given as [tex]\(25 \, \text{m/s}^2\)[/tex].
3. Apply the formula [tex]\(F = ma\)[/tex]:
The formula for force [tex]\( F \)[/tex] is given by [tex]\( F = ma \)[/tex], where:
- [tex]\(m\)[/tex] is the mass
- [tex]\(a\)[/tex] is the acceleration
4. Calculate the force:
Substitute the mass [tex]\(0.14 \text{ kg}\)[/tex] and the acceleration [tex]\(25 \, \text{m/s}^2\)[/tex] into the formula:
[tex]\[
F = 0.14 \text{ kg} \times 25 \, \text{m/s}^2
\][/tex]
[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:
3.5 N.
1. Determine the mass in kilograms:
The mass of the ball is given in grams (140 g). We need to convert this mass to kilograms because the standard unit of mass in physics calculations is kilograms (kg).
- Conversion factor: [tex]\( 1 \text{ kg} = 1000 \text{ g} \)[/tex]
- Therefore, [tex]\(140 \text{ g} = \frac{140}{1000} \text{ kg} = 0.14 \text{ kg}\)[/tex]
2. Identify the acceleration:
The acceleration is given as [tex]\(25 \, \text{m/s}^2\)[/tex].
3. Apply the formula [tex]\(F = ma\)[/tex]:
The formula for force [tex]\( F \)[/tex] is given by [tex]\( F = ma \)[/tex], where:
- [tex]\(m\)[/tex] is the mass
- [tex]\(a\)[/tex] is the acceleration
4. Calculate the force:
Substitute the mass [tex]\(0.14 \text{ kg}\)[/tex] and the acceleration [tex]\(25 \, \text{m/s}^2\)[/tex] into the formula:
[tex]\[
F = 0.14 \text{ kg} \times 25 \, \text{m/s}^2
\][/tex]
[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:
3.5 N.
