Answer :
To solve this problem, we'll use the formula for force, which is given by:
[tex]\[ F = m \times a \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( a \)[/tex] is the acceleration.
Step-by-Step Solution:
1. Understand the Given Information:
- The mass of the ball is 140 grams.
- The acceleration is [tex]\( 25 \, \text{m/s}^2 \)[/tex].
2. Convert Units:
- Since standard units of mass in physics are in kilograms (kg), we need to convert 140 grams to kilograms.
- To convert grams to kilograms, we use the conversion factor [tex]\( 1 \, \text{kg} = 1000 \, \text{g} \)[/tex].
[tex]\[
\text{Mass in kg} = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg}
\][/tex]
3. Calculate the Force:
- Use the formula with the converted mass and the given acceleration.
[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 at [tex]\( 25 \, \text{m/s}^2 \)[/tex] is [tex]\( 3.5 \, \text{N} \)[/tex].
[tex]\[ F = m \times a \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( a \)[/tex] is the acceleration.
Step-by-Step Solution:
1. Understand the Given Information:
- The mass of the ball is 140 grams.
- The acceleration is [tex]\( 25 \, \text{m/s}^2 \)[/tex].
2. Convert Units:
- Since standard units of mass in physics are in kilograms (kg), we need to convert 140 grams to kilograms.
- To convert grams to kilograms, we use the conversion factor [tex]\( 1 \, \text{kg} = 1000 \, \text{g} \)[/tex].
[tex]\[
\text{Mass in kg} = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg}
\][/tex]
3. Calculate the Force:
- Use the formula with the converted mass and the given acceleration.
[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 at [tex]\( 25 \, \text{m/s}^2 \)[/tex] is [tex]\( 3.5 \, \text{N} \)[/tex].
