Answer :
To find the force needed to accelerate a ball with a mass of 140 grams at an acceleration of 25 m/s², you 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 (m/s²).
Here are the steps to solve the problem:
1. Convert the mass from grams to kilograms:
The given mass is 140 grams. To convert grams to kilograms, you divide by 1000 because there are 1000 grams in a kilogram.
[tex]\[ m = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg} \][/tex]
2. Use the formula to calculate the force:
With the mass in kilograms and the acceleration given as 25 m/s², substitute these values into the formula.
[tex]\[ F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 \][/tex]
[tex]\[ F = 3.5 \, \text{N} \][/tex]
Therefore, the force needed to accelerate the ball is 3.5 N.
[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 (m/s²).
Here are the steps to solve the problem:
1. Convert the mass from grams to kilograms:
The given mass is 140 grams. To convert grams to kilograms, you divide by 1000 because there are 1000 grams in a kilogram.
[tex]\[ m = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg} \][/tex]
2. Use the formula to calculate the force:
With the mass in kilograms and the acceleration given as 25 m/s², substitute these values into the formula.
[tex]\[ F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 \][/tex]
[tex]\[ F = 3.5 \, \text{N} \][/tex]
Therefore, the force needed to accelerate the ball is 3.5 N.
