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Answer :
To find 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 [tex]\(F = ma\)[/tex], where [tex]\(F\)[/tex] is the force, [tex]\(m\)[/tex] is the mass, and [tex]\(a\)[/tex] is the acceleration.
Here is the step-by-step solution:
1. Convert mass to kilograms:
The mass of the ball is given as 140 grams. We need to convert this to kilograms because the standard unit for mass in physics is kilograms.
[tex]\[
\text{Mass in kilograms} = \frac{140 \, \text{grams}}{1000} = 0.14 \, \text{kg}
\][/tex]
2. Use the formula [tex]\(F = ma\)[/tex]:
Substitute the values for mass and acceleration into the formula.
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2
\][/tex]
3. Calculate the force:
Performing the multiplication gives:
[tex]\[
F = 3.5 \, \text{N}
\][/tex]
Therefore, the force needed to accelerate the ball at [tex]\(25 \, \text{m/s}^2\)[/tex] is [tex]\(3.5 \, \text{N}\)[/tex]. The correct answer is [tex]\(3.5 \, \text{N}\)[/tex].
Here is the step-by-step solution:
1. Convert mass to kilograms:
The mass of the ball is given as 140 grams. We need to convert this to kilograms because the standard unit for mass in physics is kilograms.
[tex]\[
\text{Mass in kilograms} = \frac{140 \, \text{grams}}{1000} = 0.14 \, \text{kg}
\][/tex]
2. Use the formula [tex]\(F = ma\)[/tex]:
Substitute the values for mass and acceleration into the formula.
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2
\][/tex]
3. Calculate the force:
Performing the multiplication gives:
[tex]\[
F = 3.5 \, \text{N}
\][/tex]
Therefore, the force needed to accelerate the ball at [tex]\(25 \, \text{m/s}^2\)[/tex] is [tex]\(3.5 \, \text{N}\)[/tex]. The correct answer is [tex]\(3.5 \, \text{N}\)[/tex].
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