Answer :
To solve this problem, we need to determine the force required to accelerate a ball with a mass of 140 grams at an acceleration of [tex]\(25 \, \text{m/s}^2\)[/tex].
Here are the steps to find the solution:
1. Convert the mass from grams to kilograms.
The mass of the ball is given as 140 grams. Since the standard unit of mass in physics is kilograms (kg), we need to convert grams to kilograms.
[tex]\[
1 \, \text{kg} = 1000 \, \text{g}
\][/tex]
Therefore, the mass in kilograms is:
[tex]\[
\text{mass in kg} = \frac{140}{1000} = 0.14 \, \text{kg}
\][/tex]
2. Apply the formula for force.
The formula that relates force, mass, and acceleration is:
[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),
- [tex]\( a \)[/tex] is the acceleration in meters per second squared ([tex]\( \text{m/s}^2 \)[/tex]).
Plug the values into the formula:
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2
\][/tex]
3. Calculate the force.
[tex]\[
F = 3.5 \, \text{N}
\][/tex]
The force needed to accelerate the ball at [tex]\(25 \, \text{m/s}^2\)[/tex] is [tex]\(3.5 \, \text{N}\)[/tex].
So, the correct answer is [tex]\(3.5 \, \text{N}\)[/tex].
Here are the steps to find the solution:
1. Convert the mass from grams to kilograms.
The mass of the ball is given as 140 grams. Since the standard unit of mass in physics is kilograms (kg), we need to convert grams to kilograms.
[tex]\[
1 \, \text{kg} = 1000 \, \text{g}
\][/tex]
Therefore, the mass in kilograms is:
[tex]\[
\text{mass in kg} = \frac{140}{1000} = 0.14 \, \text{kg}
\][/tex]
2. Apply the formula for force.
The formula that relates force, mass, and acceleration is:
[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),
- [tex]\( a \)[/tex] is the acceleration in meters per second squared ([tex]\( \text{m/s}^2 \)[/tex]).
Plug the values into the formula:
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2
\][/tex]
3. Calculate the force.
[tex]\[
F = 3.5 \, \text{N}
\][/tex]
The force needed to accelerate the ball at [tex]\(25 \, \text{m/s}^2\)[/tex] is [tex]\(3.5 \, \text{N}\)[/tex].
So, the correct answer is [tex]\(3.5 \, \text{N}\)[/tex].
