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.
1. Convert the mass from grams to kilograms:
Since the mass is given in grams, convert it to kilograms because the standard unit of mass in physics is kilograms.
[tex]\[
m = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg}
\][/tex]
2. Use the formula [tex]\(F = ma\)[/tex]:
Substitute the mass in kilograms and the acceleration into the formula.
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2
\][/tex]
3. Calculate the force:
Perform the multiplication to find the force.
[tex]\[
F = 3.5 \, \text{N}
\][/tex]
So, the force needed to accelerate the ball is [tex]\(3.5 \, \text{N}\)[/tex]. Therefore, the correct answer is [tex]\(3.5 \, \text{N}\)[/tex].
1. Convert the mass from grams to kilograms:
Since the mass is given in grams, convert it to kilograms because the standard unit of mass in physics is kilograms.
[tex]\[
m = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg}
\][/tex]
2. Use the formula [tex]\(F = ma\)[/tex]:
Substitute the mass in kilograms and the acceleration into the formula.
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2
\][/tex]
3. Calculate the force:
Perform the multiplication to find the force.
[tex]\[
F = 3.5 \, \text{N}
\][/tex]
So, the force needed to accelerate the ball is [tex]\(3.5 \, \text{N}\)[/tex]. Therefore, the correct answer is [tex]\(3.5 \, \text{N}\)[/tex].
