Answer :
To determine the force needed to accelerate the ball, we use the formula:
[tex]\[ F = m \times a \][/tex]
Where:
- [tex]\( F \)[/tex] is the force
- [tex]\( m \)[/tex] is the mass
- [tex]\( a \)[/tex] is the acceleration
Here's the step-by-step solution:
1. Convert the mass from grams to kilograms:
- Given the mass [tex]\( m = 140 \)[/tex] grams
- Since [tex]\( 1 \)[/tex] kilogram [tex]\( = 1000 \)[/tex] grams, we convert the mass as follows:
[tex]\[ m = \frac{140 \text{ grams}}{1000} = 0.14 \text{ kilograms} \][/tex]
2. Use the acceleration as given:
- The acceleration [tex]\( a = 25 \)[/tex] meters per second squared [tex]\((m/s^2)\)[/tex]
3. Calculate the force:
- Plug the values into the formula [tex]\( F = m \times a \)[/tex]
[tex]\[ F = 0.14 \text{ kg} \times 25 \text{ m/s}^2 = 3.5 \text{ N} \][/tex]
Therefore, the force needed to accelerate the ball at [tex]\( 25 \, m/s^2 \)[/tex] is [tex]\( 3.5 \)[/tex] Newtons.
The correct answer is:
[tex]\[ 3.5 \, \text{N} \][/tex]
[tex]\[ F = m \times a \][/tex]
Where:
- [tex]\( F \)[/tex] is the force
- [tex]\( m \)[/tex] is the mass
- [tex]\( a \)[/tex] is the acceleration
Here's the step-by-step solution:
1. Convert the mass from grams to kilograms:
- Given the mass [tex]\( m = 140 \)[/tex] grams
- Since [tex]\( 1 \)[/tex] kilogram [tex]\( = 1000 \)[/tex] grams, we convert the mass as follows:
[tex]\[ m = \frac{140 \text{ grams}}{1000} = 0.14 \text{ kilograms} \][/tex]
2. Use the acceleration as given:
- The acceleration [tex]\( a = 25 \)[/tex] meters per second squared [tex]\((m/s^2)\)[/tex]
3. Calculate the force:
- Plug the values into the formula [tex]\( F = m \times a \)[/tex]
[tex]\[ F = 0.14 \text{ kg} \times 25 \text{ m/s}^2 = 3.5 \text{ N} \][/tex]
Therefore, the force needed to accelerate the ball at [tex]\( 25 \, m/s^2 \)[/tex] is [tex]\( 3.5 \)[/tex] Newtons.
The correct answer is:
[tex]\[ 3.5 \, \text{N} \][/tex]
