Answer :
To solve this problem, we need to find the force required to accelerate a ball with a given mass. The formula to find force is:
[tex]\[ F = ma \][/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]\( m/s^2 \)[/tex]).
### Step-by-Step Solution
1. Convert the Mass:
- The mass of the ball is given as 140 grams. Since the standard unit of mass in this context is kilograms, we need to convert grams to kilograms.
- To convert grams to kilograms, divide by 1000:
[tex]\[
m = \frac{140 \, \text{grams}}{1000} = 0.14 \, \text{kg}
\][/tex]
2. Use the Given Acceleration:
- The acceleration provided is [tex]\( 25 \, m/s^2 \)[/tex].
3. Calculate the Force:
- Apply the formula [tex]\( F = ma \)[/tex]:
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, m/s^2
\][/tex]
- Calculate the product:
[tex]\[
F = 3.5 \, \text{N}
\][/tex]
The force needed to accelerate the ball is [tex]\( 3.5 \, \text{N} \)[/tex]. Therefore, the correct answer is 3.5 N.
[tex]\[ F = ma \][/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]\( m/s^2 \)[/tex]).
### Step-by-Step Solution
1. Convert the Mass:
- The mass of the ball is given as 140 grams. Since the standard unit of mass in this context is kilograms, we need to convert grams to kilograms.
- To convert grams to kilograms, divide by 1000:
[tex]\[
m = \frac{140 \, \text{grams}}{1000} = 0.14 \, \text{kg}
\][/tex]
2. Use the Given Acceleration:
- The acceleration provided is [tex]\( 25 \, m/s^2 \)[/tex].
3. Calculate the Force:
- Apply the formula [tex]\( F = ma \)[/tex]:
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, m/s^2
\][/tex]
- Calculate the product:
[tex]\[
F = 3.5 \, \text{N}
\][/tex]
The force needed to accelerate the ball is [tex]\( 3.5 \, \text{N} \)[/tex]. Therefore, the correct answer is 3.5 N.
