Answer :
To solve the problem of finding 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 can use the formula for force:
[tex]\[ F = m \times a \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( a \)[/tex] is the acceleration.
### Step-by-step Solution:
1. Convert the Mass from Grams to Kilograms:
The mass of the ball is given as 140 grams. We need to convert this mass into kilograms because the standard unit for mass in the formula is kilograms.
[tex]\[
\text{Mass in kilograms} = \frac{\text{Mass in grams}}{1000} = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg}
\][/tex]
2. Identify the Acceleration:
The acceleration provided in the question is [tex]\(25 \, \text{m/s}^2\)[/tex].
3. Apply the Formula:
Substituting the values of mass and acceleration into the formula [tex]\(F = m \times a\)[/tex]:
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 = 3.5 \, \text{N}
\][/tex]
Therefore, the force needed to accelerate the ball is [tex]\(3.5 \, \text{N}\)[/tex]. The correct answer to the question is 3.5 N.
[tex]\[ F = m \times a \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( a \)[/tex] is the acceleration.
### Step-by-step Solution:
1. Convert the Mass from Grams to Kilograms:
The mass of the ball is given as 140 grams. We need to convert this mass into kilograms because the standard unit for mass in the formula is kilograms.
[tex]\[
\text{Mass in kilograms} = \frac{\text{Mass in grams}}{1000} = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg}
\][/tex]
2. Identify the Acceleration:
The acceleration provided in the question is [tex]\(25 \, \text{m/s}^2\)[/tex].
3. Apply the Formula:
Substituting the values of mass and acceleration into the formula [tex]\(F = m \times a\)[/tex]:
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 = 3.5 \, \text{N}
\][/tex]
Therefore, the force needed to accelerate the ball is [tex]\(3.5 \, \text{N}\)[/tex]. The correct answer to the question is 3.5 N.
