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Answer :
To find the force needed to accelerate a ball with a mass of 140 grams at [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 in newtons (N), [tex]\( m \)[/tex] is the mass in kilograms (kg), and [tex]\( a \)[/tex] is the acceleration in meters per second squared ([tex]\(\text{m/s}^2\)[/tex]).
Step 1: Convert the mass from grams to kilograms
The mass is given as 140 grams. To convert grams to kilograms, we divide by 1000:
[tex]\[ 140 \, \text{g} = \frac{140}{1000} \, \text{kg} = 0.14 \, \text{kg} \][/tex]
Step 2: Use the formula to calculate the force
Now that we have the mass in kilograms, we can use the formula:
[tex]\[ F = m \times a \][/tex]
where
[tex]\[ m = 0.14 \, \text{kg} \][/tex]
[tex]\[ a = 25 \, \text{m/s}^2 \][/tex]
Substitute these values into the formula:
[tex]\[ F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 \][/tex]
[tex]\[ F = 3.5 \, \text{N} \][/tex]
Therefore, the force needed to accelerate the ball is [tex]\(3.5 \, \text{N}\)[/tex]. So, the correct answer to the question is [tex]\(3.5 \, \text{N}\)[/tex].
[tex]\[ F = m \times a \][/tex]
where [tex]\( F \)[/tex] is the force in newtons (N), [tex]\( m \)[/tex] is the mass in kilograms (kg), and [tex]\( a \)[/tex] is the acceleration in meters per second squared ([tex]\(\text{m/s}^2\)[/tex]).
Step 1: Convert the mass from grams to kilograms
The mass is given as 140 grams. To convert grams to kilograms, we divide by 1000:
[tex]\[ 140 \, \text{g} = \frac{140}{1000} \, \text{kg} = 0.14 \, \text{kg} \][/tex]
Step 2: Use the formula to calculate the force
Now that we have the mass in kilograms, we can use the formula:
[tex]\[ F = m \times a \][/tex]
where
[tex]\[ m = 0.14 \, \text{kg} \][/tex]
[tex]\[ a = 25 \, \text{m/s}^2 \][/tex]
Substitute these values into the formula:
[tex]\[ F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 \][/tex]
[tex]\[ F = 3.5 \, \text{N} \][/tex]
Therefore, the force needed to accelerate the ball is [tex]\(3.5 \, \text{N}\)[/tex]. So, the correct answer to the question is [tex]\(3.5 \, \text{N}\)[/tex].
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