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Answer :
First, let's analyze the given problem step-by-step:
1. Mass Conversion:
The mass of the ball is given in grams (g). However, the standard unit of mass in the context of the force formula [tex]\( F = ma \)[/tex] (where [tex]\( F \)[/tex] is force, [tex]\( m \)[/tex] is mass, and [tex]\( a \)[/tex] is acceleration) should be in kilograms (kg).
- Given mass, [tex]\( 140 \)[/tex] grams.
- Convert grams to kilograms:
[tex]\[
140 \, \text{grams} = \frac{140}{1000} \, \text{kilograms} = 0.14 \, \text{kilograms}
\][/tex]
2. Acceleration:
The acceleration is given directly in meters per second squared ([tex]\( m/s^2 \)[/tex]).
- Given acceleration, [tex]\( a = 25 \, m/s^2 \)[/tex].
3. Apply the Formula [tex]\( F = ma \)[/tex]:
Now, use the formula for force:
[tex]\[
F = ma
\][/tex]
- Mass [tex]\( m = 0.14 \, \text{kg} \)[/tex].
- Acceleration [tex]\( a = 25 \, m/s^2 \)[/tex].
Therefore,
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, m/s^2 = 3.5 \, \text{N}
\][/tex]
4. Conclusion:
The force needed to accelerate the ball at [tex]\( 25 \, m/s^2 \)[/tex] is [tex]\( 3.5 \, \text{N} \)[/tex].
Among the multiple-choice options provided:
- 3.5 N
- 115 N
- 165 N
- 4.5 N
The correct answer is [tex]\( 3.5 \, \text{N} \)[/tex].
1. Mass Conversion:
The mass of the ball is given in grams (g). However, the standard unit of mass in the context of the force formula [tex]\( F = ma \)[/tex] (where [tex]\( F \)[/tex] is force, [tex]\( m \)[/tex] is mass, and [tex]\( a \)[/tex] is acceleration) should be in kilograms (kg).
- Given mass, [tex]\( 140 \)[/tex] grams.
- Convert grams to kilograms:
[tex]\[
140 \, \text{grams} = \frac{140}{1000} \, \text{kilograms} = 0.14 \, \text{kilograms}
\][/tex]
2. Acceleration:
The acceleration is given directly in meters per second squared ([tex]\( m/s^2 \)[/tex]).
- Given acceleration, [tex]\( a = 25 \, m/s^2 \)[/tex].
3. Apply the Formula [tex]\( F = ma \)[/tex]:
Now, use the formula for force:
[tex]\[
F = ma
\][/tex]
- Mass [tex]\( m = 0.14 \, \text{kg} \)[/tex].
- Acceleration [tex]\( a = 25 \, m/s^2 \)[/tex].
Therefore,
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, m/s^2 = 3.5 \, \text{N}
\][/tex]
4. Conclusion:
The force needed to accelerate the ball at [tex]\( 25 \, m/s^2 \)[/tex] is [tex]\( 3.5 \, \text{N} \)[/tex].
Among the multiple-choice options provided:
- 3.5 N
- 115 N
- 165 N
- 4.5 N
The correct answer is [tex]\( 3.5 \, \text{N} \)[/tex].
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