Answer :
To solve this problem, we need to calculate the force required to accelerate a ball with a known mass at a specific acceleration. We use the formula:
[tex]\[ F = ma \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass of the ball,
- [tex]\( a \)[/tex] is the acceleration.
Here are the steps to find the solution:
1. Convert the Mass to Kilograms:
The mass of the ball is given as 140 grams. We need to convert this mass into kilograms because the standard unit for mass in physics formulas is kilograms (kg).
[tex]\[
\text{mass in kg} = \frac{140 \text{ g}}{1000} = 0.14 \text{ kg}
\][/tex]
2. Use the Formula [tex]\( F = ma \)[/tex]:
The acceleration [tex]\( a \)[/tex] is given as 25 meters per second squared (m/s²). Now, we can substitute the values into the formula:
[tex]\[
F = 0.14 \text{ kg} \times 25 \text{ m/s}^2
\][/tex]
3. Calculate the Force:
Multiply the mass by the acceleration to find the force.
[tex]\[
F = 0.14 \times 25 = 3.5 \text{ N}
\][/tex]
Therefore, the force needed to accelerate the ball at 25 m/s² is 3.5 newtons (N). So, the correct answer is 3.5 N.
[tex]\[ F = ma \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass of the ball,
- [tex]\( a \)[/tex] is the acceleration.
Here are the steps to find the solution:
1. Convert the Mass to Kilograms:
The mass of the ball is given as 140 grams. We need to convert this mass into kilograms because the standard unit for mass in physics formulas is kilograms (kg).
[tex]\[
\text{mass in kg} = \frac{140 \text{ g}}{1000} = 0.14 \text{ kg}
\][/tex]
2. Use the Formula [tex]\( F = ma \)[/tex]:
The acceleration [tex]\( a \)[/tex] is given as 25 meters per second squared (m/s²). Now, we can substitute the values into the formula:
[tex]\[
F = 0.14 \text{ kg} \times 25 \text{ m/s}^2
\][/tex]
3. Calculate the Force:
Multiply the mass by the acceleration to find the force.
[tex]\[
F = 0.14 \times 25 = 3.5 \text{ N}
\][/tex]
Therefore, the force needed to accelerate the ball at 25 m/s² is 3.5 newtons (N). So, the correct answer is 3.5 N.
