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Answer :
To find the force needed to accelerate a ball with a mass of 140 g at 25 m/s², we can use the formula:
[tex]\[ F = ma \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( a \)[/tex] is the acceleration.
Step 1: Convert the mass from grams to kilograms.
Since 1 gram is equal to 0.001 kilograms, we convert 140 grams to kilograms:
[tex]\[ 140 \, \text{g} = 140 \times 0.001 \, \text{kg} = 0.14 \, \text{kg} \][/tex]
Step 2: Plug the values into the formula.
Now, substitute the mass ([tex]\( m = 0.14 \, \text{kg} \)[/tex]) and the acceleration ([tex]\( a = 25 \, \text{m/s}^2 \)[/tex]) into the formula:
[tex]\[ F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 \][/tex]
Step 3: Calculate the force.
By multiplying the mass and the acceleration, we get:
[tex]\[ F = 3.5 \, \text{N} \][/tex]
So, the force needed to accelerate the ball at 25 m/s² is [tex]\( 3.5 \, \text{N} \)[/tex].
Therefore, the correct answer is [tex]\( \boxed{3.5 \, \text{N}} \)[/tex].
[tex]\[ F = ma \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( a \)[/tex] is the acceleration.
Step 1: Convert the mass from grams to kilograms.
Since 1 gram is equal to 0.001 kilograms, we convert 140 grams to kilograms:
[tex]\[ 140 \, \text{g} = 140 \times 0.001 \, \text{kg} = 0.14 \, \text{kg} \][/tex]
Step 2: Plug the values into the formula.
Now, substitute the mass ([tex]\( m = 0.14 \, \text{kg} \)[/tex]) and the acceleration ([tex]\( a = 25 \, \text{m/s}^2 \)[/tex]) into the formula:
[tex]\[ F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 \][/tex]
Step 3: Calculate the force.
By multiplying the mass and the acceleration, we get:
[tex]\[ F = 3.5 \, \text{N} \][/tex]
So, the force needed to accelerate the ball at 25 m/s² is [tex]\( 3.5 \, \text{N} \)[/tex].
Therefore, the correct answer is [tex]\( \boxed{3.5 \, \text{N}} \)[/tex].
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