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Answer :
To determine 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 of the object,
- [tex]\( a \)[/tex] is the acceleration.
Step 1: Convert the mass from grams to kilograms
The mass of the ball is given as 140 grams. Since we need the mass in kilograms for the formula, we convert it:
[tex]\[ 140 \, \text{g} = 140 \, \text{g} \times \frac{1 \, \text{kg}}{1000 \, \text{g}} = 0.14 \, \text{kg} \][/tex]
Step 2: Use the formula [tex]\( F = m \times a \)[/tex]
Now, with the mass in kilograms and the given acceleration, we can plug in the values:
[tex]\[ F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 \][/tex]
Step 3: Calculate the force
[tex]\[ F = 3.5 \, \text{N} \][/tex]
So, the force needed to accelerate the ball at [tex]\(25 \, \text{m/s}^2\)[/tex] is 3.5 N.
[tex]\[ F = m \times a \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( a \)[/tex] is the acceleration.
Step 1: Convert the mass from grams to kilograms
The mass of the ball is given as 140 grams. Since we need the mass in kilograms for the formula, we convert it:
[tex]\[ 140 \, \text{g} = 140 \, \text{g} \times \frac{1 \, \text{kg}}{1000 \, \text{g}} = 0.14 \, \text{kg} \][/tex]
Step 2: Use the formula [tex]\( F = m \times a \)[/tex]
Now, with the mass in kilograms and the given acceleration, we can plug in the values:
[tex]\[ F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 \][/tex]
Step 3: Calculate the force
[tex]\[ F = 3.5 \, \text{N} \][/tex]
So, the force needed to accelerate the ball at [tex]\(25 \, \text{m/s}^2\)[/tex] is 3.5 N.
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