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Answer :
To find the force needed to accelerate the ball, we can use the formula:
[tex]\[ F = m \times a \][/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]).
1. Convert the mass from grams to kilograms:
- The mass of the ball is 140 grams.
- To convert grams to kilograms, we divide by 1000 because there are 1000 grams in a kilogram.
[tex]\[
m = \frac{140}{1000} = 0.14 \text{ kg}
\][/tex]
2. Use the formula to calculate the force:
- The acceleration given is [tex]\( 25 \, m/s^2 \)[/tex].
- Substitute the mass in kilograms and the acceleration into the formula:
[tex]\[
F = 0.14 \times 25
\][/tex]
3. Calculate the result:
[tex]\[
F = 3.5 \text{ N}
\][/tex]
Therefore, the force needed to accelerate the ball is [tex]\( 3.5 \, \text{N} \)[/tex]. The correct answer is [tex]\( 3.5 \, \text{N} \)[/tex].
[tex]\[ F = m \times a \][/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]).
1. Convert the mass from grams to kilograms:
- The mass of the ball is 140 grams.
- To convert grams to kilograms, we divide by 1000 because there are 1000 grams in a kilogram.
[tex]\[
m = \frac{140}{1000} = 0.14 \text{ kg}
\][/tex]
2. Use the formula to calculate the force:
- The acceleration given is [tex]\( 25 \, m/s^2 \)[/tex].
- Substitute the mass in kilograms and the acceleration into the formula:
[tex]\[
F = 0.14 \times 25
\][/tex]
3. Calculate the result:
[tex]\[
F = 3.5 \text{ N}
\][/tex]
Therefore, the force needed to accelerate the ball is [tex]\( 3.5 \, \text{N} \)[/tex]. The correct answer is [tex]\( 3.5 \, \text{N} \)[/tex].
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