Answer :
Sure, let's go step by step to solve this problem.
### Step 1: Identify the given values.
- Mass of the ball [tex]\( m \)[/tex] is 140 grams.
- Acceleration [tex]\( a \)[/tex] is [tex]\( 25 \, \text{m/s}^2 \)[/tex].
### Step 2: Convert the mass from grams to kilograms.
Since the standard unit of mass in the formula [tex]\( F = ma \)[/tex] is kilograms (kg), we need to convert grams to kilograms.
- [tex]\( 1 \, \text{kg} = 1000 \, \text{g} \)[/tex].
- Therefore, [tex]\( 140 \, \text{g} = 140 / 1000 = 0.14 \, \text{kg} \)[/tex].
### Step 3: Apply the formula [tex]\( F = ma \)[/tex].
We use the formula [tex]\( F = ma \)[/tex] where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass in kilograms,
- [tex]\( a \)[/tex] is the acceleration in [tex]\( \text{m/s}^2 \)[/tex].
Plugging in the values:
[tex]\[ F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 \][/tex]
### Step 4: Calculate the force.
[tex]\[ F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 = 3.5 \, \text{N} \][/tex]
So, the force needed to accelerate the ball is [tex]\( \bf{3.5 \, \text{N}} \)[/tex]. This matches one of the provided options. Therefore, the correct answer is:
[tex]\[
\boxed{3.5 \, \text{N}}
\][/tex]
### Step 1: Identify the given values.
- Mass of the ball [tex]\( m \)[/tex] is 140 grams.
- Acceleration [tex]\( a \)[/tex] is [tex]\( 25 \, \text{m/s}^2 \)[/tex].
### Step 2: Convert the mass from grams to kilograms.
Since the standard unit of mass in the formula [tex]\( F = ma \)[/tex] is kilograms (kg), we need to convert grams to kilograms.
- [tex]\( 1 \, \text{kg} = 1000 \, \text{g} \)[/tex].
- Therefore, [tex]\( 140 \, \text{g} = 140 / 1000 = 0.14 \, \text{kg} \)[/tex].
### Step 3: Apply the formula [tex]\( F = ma \)[/tex].
We use the formula [tex]\( F = ma \)[/tex] where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass in kilograms,
- [tex]\( a \)[/tex] is the acceleration in [tex]\( \text{m/s}^2 \)[/tex].
Plugging in the values:
[tex]\[ F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 \][/tex]
### Step 4: Calculate the force.
[tex]\[ F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 = 3.5 \, \text{N} \][/tex]
So, the force needed to accelerate the ball is [tex]\( \bf{3.5 \, \text{N}} \)[/tex]. This matches one of the provided options. Therefore, the correct answer is:
[tex]\[
\boxed{3.5 \, \text{N}}
\][/tex]
