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Answer :
To find the force needed to accelerate the ball, we use the formula:
[tex]\[ F = ma \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass of the object, and
- [tex]\( a \)[/tex] is the acceleration.
Step-by-step Solution:
1. Convert the mass from grams to kilograms:
The mass of the ball is given as 140 grams. To convert this to kilograms (since the standard unit of mass in physics is kilograms), we divide by 1000:
[tex]\[
m = \frac{140}{1000} = 0.14 \text{ kg}
\][/tex]
2. Use the given acceleration:
The acceleration is given as 25 m/s².
3. Substitute the values into the formula:
[tex]\[
F = ma = 0.14 \text{ kg} \times 25 \text{ m/s}^2
\][/tex]
4. Calculate the force:
[tex]\[
F = 3.5 \text{ N}
\][/tex]
So, the force needed to accelerate the ball at 25 m/s² is 3.5 N.
[tex]\[ F = ma \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass of the object, and
- [tex]\( a \)[/tex] is the acceleration.
Step-by-step Solution:
1. Convert the mass from grams to kilograms:
The mass of the ball is given as 140 grams. To convert this to kilograms (since the standard unit of mass in physics is kilograms), we divide by 1000:
[tex]\[
m = \frac{140}{1000} = 0.14 \text{ kg}
\][/tex]
2. Use the given acceleration:
The acceleration is given as 25 m/s².
3. Substitute the values into the formula:
[tex]\[
F = ma = 0.14 \text{ kg} \times 25 \text{ m/s}^2
\][/tex]
4. Calculate the force:
[tex]\[
F = 3.5 \text{ N}
\][/tex]
So, the force needed to accelerate the ball at 25 m/s² is 3.5 N.
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