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Answer :
To determine the force needed to accelerate a ball, we can use the formula:
[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).
Here are the steps to find the solution:
1. Convert Mass to Kilograms:
The mass of the ball is given as 140 grams. Since the standard unit for mass in this formula is kilograms, we need to convert grams to kilograms.
[tex]\[ 140 \text{ grams} = \frac{140}{1000} \text{ kg} = 0.14 \text{ kg} \][/tex]
2. Identify the Acceleration:
The acceleration given is [tex]\( 25 \text{ m/s}^2 \)[/tex].
3. Calculate the Force:
Use the formula [tex]\( F = ma \)[/tex] to calculate the force.
[tex]\[ F = 0.14 \text{ kg} \times 25 \text{ m/s}^2 = 3.5 \text{ N} \][/tex]
So, the force needed to accelerate the ball at [tex]\( 25 \text{ m/s}^2 \)[/tex] is [tex]\( 3.5 \text{ N} \)[/tex]. This is the correct option from the given choices.
[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).
Here are the steps to find the solution:
1. Convert Mass to Kilograms:
The mass of the ball is given as 140 grams. Since the standard unit for mass in this formula is kilograms, we need to convert grams to kilograms.
[tex]\[ 140 \text{ grams} = \frac{140}{1000} \text{ kg} = 0.14 \text{ kg} \][/tex]
2. Identify the Acceleration:
The acceleration given is [tex]\( 25 \text{ m/s}^2 \)[/tex].
3. Calculate the Force:
Use the formula [tex]\( F = ma \)[/tex] to calculate the force.
[tex]\[ F = 0.14 \text{ kg} \times 25 \text{ m/s}^2 = 3.5 \text{ N} \][/tex]
So, the force needed to accelerate the ball at [tex]\( 25 \text{ m/s}^2 \)[/tex] is [tex]\( 3.5 \text{ N} \)[/tex]. This is the correct option from the given choices.
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