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Answer :
To find the force needed to accelerate the ball, we use the formula for force:
[tex]\[ F = ma \][/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 (m/s²).
Here's how you solve the problem step-by-step:
1. Convert the mass from grams to kilograms.
The mass of the ball is given as 140 grams. We need to convert this to kilograms because the standard unit of mass in physics is kilograms. To convert grams to kilograms, divide by 1000.
[tex]\[
m = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg}
\][/tex]
2. Use the formula to calculate the force.
The acceleration is given as [tex]\( 25 \, \text{m/s}^2 \)[/tex].
Substitute the values into the formula:
[tex]\[
F = ma = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2
\][/tex]
[tex]\[
F = 3.5 \, \text{N}
\][/tex]
Thus, the force needed to accelerate the ball at [tex]\( 25 \, \text{m/s}^2 \)[/tex] is [tex]\( 3.5 \, \text{N} \)[/tex].
[tex]\[ F = ma \][/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 (m/s²).
Here's how you solve the problem step-by-step:
1. Convert the mass from grams to kilograms.
The mass of the ball is given as 140 grams. We need to convert this to kilograms because the standard unit of mass in physics is kilograms. To convert grams to kilograms, divide by 1000.
[tex]\[
m = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg}
\][/tex]
2. Use the formula to calculate the force.
The acceleration is given as [tex]\( 25 \, \text{m/s}^2 \)[/tex].
Substitute the values into the formula:
[tex]\[
F = ma = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2
\][/tex]
[tex]\[
F = 3.5 \, \text{N}
\][/tex]
Thus, the force needed to accelerate the ball at [tex]\( 25 \, \text{m/s}^2 \)[/tex] is [tex]\( 3.5 \, \text{N} \)[/tex].
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