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Answer :
Sure! Let's break down the problem step-by-step to understand how to find the force needed to accelerate the ball.
1. Identify the given values:
- Mass of the ball ([tex]\( m \)[/tex]) = 140 grams
- Acceleration ([tex]\( a \)[/tex]) = 25 [tex]\( m/s^2 \)[/tex]
2. Convert the mass from grams to kilograms:
- We know that 1 kilogram = 1000 grams.
- Therefore, the mass of the ball in kilograms is [tex]\( \frac{140 \text{ grams}}{1000 \text{ grams/kilogram}} = 0.14 \text{ kilograms} \)[/tex].
3. Use the formula for force:
- The formula to calculate force is [tex]\( F = ma \)[/tex], where [tex]\( F \)[/tex] is the force, [tex]\( m \)[/tex] is the mass, and [tex]\( a \)[/tex] is the acceleration.
4. Substitute the values into the formula:
- Mass ([tex]\( m \)[/tex]) = 0.14 kilograms
- Acceleration ([tex]\( a \)[/tex]) = 25 [tex]\( m/s^2 \)[/tex]
- So, [tex]\( F = 0.14 \times 25 \)[/tex]
5. Perform the multiplication:
- [tex]\( F = 0.14 \times 25 = 3.5 \text{ Newtons} \)[/tex]
Therefore, the force needed to accelerate the ball at [tex]\( 25 \, m/s^2 \)[/tex] is [tex]\( 3.5 \)[/tex] Newtons.
The correct answer among the options provided is:
3.5 N
1. Identify the given values:
- Mass of the ball ([tex]\( m \)[/tex]) = 140 grams
- Acceleration ([tex]\( a \)[/tex]) = 25 [tex]\( m/s^2 \)[/tex]
2. Convert the mass from grams to kilograms:
- We know that 1 kilogram = 1000 grams.
- Therefore, the mass of the ball in kilograms is [tex]\( \frac{140 \text{ grams}}{1000 \text{ grams/kilogram}} = 0.14 \text{ kilograms} \)[/tex].
3. Use the formula for force:
- The formula to calculate force is [tex]\( F = ma \)[/tex], where [tex]\( F \)[/tex] is the force, [tex]\( m \)[/tex] is the mass, and [tex]\( a \)[/tex] is the acceleration.
4. Substitute the values into the formula:
- Mass ([tex]\( m \)[/tex]) = 0.14 kilograms
- Acceleration ([tex]\( a \)[/tex]) = 25 [tex]\( m/s^2 \)[/tex]
- So, [tex]\( F = 0.14 \times 25 \)[/tex]
5. Perform the multiplication:
- [tex]\( F = 0.14 \times 25 = 3.5 \text{ Newtons} \)[/tex]
Therefore, the force needed to accelerate the ball at [tex]\( 25 \, m/s^2 \)[/tex] is [tex]\( 3.5 \)[/tex] Newtons.
The correct answer among the options provided is:
3.5 N
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