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Answer :
To find the force needed to accelerate the ball, we can use the formula [tex]\( F = ma \)[/tex], where [tex]\( F \)[/tex] is the force, [tex]\( m \)[/tex] is the mass, and [tex]\( a \)[/tex] is the acceleration.
Here's how you solve it step-by-step:
1. Convert the mass to kilograms: The given mass of the ball is 140 grams. Since we need the mass in kilograms for the formula, we convert grams to kilograms. There are 1,000 grams in a kilogram, so:
[tex]\[
m = \frac{140}{1000} = 0.14 \text{ kg}
\][/tex]
2. Use the formula [tex]\( F = ma \)[/tex]: Now that we have the mass in kilograms, we can use the formula with the given acceleration of [tex]\( 25 \, \text{m/s}^2 \)[/tex].
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2
\][/tex]
3. Calculate the force:
[tex]\[
F = 3.5 \, \text{N}
\][/tex]
So, the force needed to accelerate the ball is [tex]\( 3.5 \, \text{N} \)[/tex].
Here's how you solve it step-by-step:
1. Convert the mass to kilograms: The given mass of the ball is 140 grams. Since we need the mass in kilograms for the formula, we convert grams to kilograms. There are 1,000 grams in a kilogram, so:
[tex]\[
m = \frac{140}{1000} = 0.14 \text{ kg}
\][/tex]
2. Use the formula [tex]\( F = ma \)[/tex]: Now that we have the mass in kilograms, we can use the formula with the given acceleration of [tex]\( 25 \, \text{m/s}^2 \)[/tex].
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2
\][/tex]
3. Calculate the force:
[tex]\[
F = 3.5 \, \text{N}
\][/tex]
So, the force needed to accelerate the ball is [tex]\( 3.5 \, \text{N} \)[/tex].
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