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Answer :
To find the force needed to accelerate a ball with a mass of 140 grams at 25 m/s², we use the formula for force:
[tex]\[ F = ma \][/tex]
where:
- [tex]\( F \)[/tex] is the force in Newtons (N),
- [tex]\( m \)[/tex] is the mass in kilograms (kg),
- [tex]\( a \)[/tex] is the acceleration in meters per second squared (m/s²).
### Step-by-Step Solution:
1. Convert Mass to Kilograms:
- The mass of the ball is given as 140 grams. To convert grams to kilograms, divide by 1000.
- [tex]\( m = \frac{140}{1000} = 0.14 \)[/tex] kg
2. Use the Formula [tex]\( F = ma \)[/tex]:
- The acceleration is given as 25 m/s².
- Substitute the values into the formula:
- [tex]\( F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 \)[/tex]
3. Calculate the Force:
- [tex]\( F = 3.5 \)[/tex] N
So, the force needed to accelerate the ball at 25 m/s² is [tex]\( 3.5 \)[/tex] Newtons.
Therefore, the correct answer is 3.5 N.
[tex]\[ F = ma \][/tex]
where:
- [tex]\( F \)[/tex] is the force in Newtons (N),
- [tex]\( m \)[/tex] is the mass in kilograms (kg),
- [tex]\( a \)[/tex] is the acceleration in meters per second squared (m/s²).
### Step-by-Step Solution:
1. Convert Mass to Kilograms:
- The mass of the ball is given as 140 grams. To convert grams to kilograms, divide by 1000.
- [tex]\( m = \frac{140}{1000} = 0.14 \)[/tex] kg
2. Use the Formula [tex]\( F = ma \)[/tex]:
- The acceleration is given as 25 m/s².
- Substitute the values into the formula:
- [tex]\( F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 \)[/tex]
3. Calculate the Force:
- [tex]\( F = 3.5 \)[/tex] N
So, the force needed to accelerate the ball at 25 m/s² is [tex]\( 3.5 \)[/tex] Newtons.
Therefore, the correct answer is 3.5 N.
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