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Answer :
To solve this problem, we need to calculate the force needed to accelerate a ball with a mass of 140 grams at an acceleration of [tex]\(25 \, \text{m/s}^2\)[/tex]. We'll use the formula for force:
[tex]\[ F = m \times a \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass of the object, and
- [tex]\( a \)[/tex] is the acceleration.
### Step-by-Step Solution:
1. Convert the Mass:
- The mass of the ball is given in grams. We need to convert it to kilograms because the standard unit of mass in physics is kilograms.
- [tex]\( 140 \, \text{grams} = 0.140 \, \text{kilograms} \)[/tex].
2. Apply the Formula:
- With the converted mass, we can now plug the values into the formula.
- [tex]\( m = 0.140 \, \text{kg} \)[/tex]
- [tex]\( a = 25 \, \text{m/s}^2 \)[/tex]
3. Calculate the Force:
[tex]\[ F = 0.140 \, \text{kg} \times 25 \, \text{m/s}^2 \][/tex]
[tex]\[ F = 3.5 \, \text{N} \][/tex]
The force needed to accelerate the ball is [tex]\(3.5 \, \text{N}\)[/tex]. This matches one of the given options. Therefore, the correct answer is [tex]\(3.5 \, \text{N}\)[/tex].
[tex]\[ F = m \times a \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass of the object, and
- [tex]\( a \)[/tex] is the acceleration.
### Step-by-Step Solution:
1. Convert the Mass:
- The mass of the ball is given in grams. We need to convert it to kilograms because the standard unit of mass in physics is kilograms.
- [tex]\( 140 \, \text{grams} = 0.140 \, \text{kilograms} \)[/tex].
2. Apply the Formula:
- With the converted mass, we can now plug the values into the formula.
- [tex]\( m = 0.140 \, \text{kg} \)[/tex]
- [tex]\( a = 25 \, \text{m/s}^2 \)[/tex]
3. Calculate the Force:
[tex]\[ F = 0.140 \, \text{kg} \times 25 \, \text{m/s}^2 \][/tex]
[tex]\[ F = 3.5 \, \text{N} \][/tex]
The force needed to accelerate the ball is [tex]\(3.5 \, \text{N}\)[/tex]. This matches one of the given options. Therefore, the correct answer is [tex]\(3.5 \, \text{N}\)[/tex].
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