Answer :
To solve the problem of determining the force needed to accelerate the ball, we'll use Newton's second law of motion. This law is expressed by 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).
### Step-by-Step Solution:
1. Identify the given values:
- The mass of the ball is 140 grams.
- The acceleration is 25 m/s².
2. Convert the mass to kilograms:
- Since 1 kilogram = 1000 grams, you need to convert the mass from grams to kilograms for it to align with the SI units (Standard International Units).
- [tex]\( 140 \text{ g} = \frac{140}{1000} \text{ kg} = 0.14 \text{ kg} \)[/tex].
3. Apply the formula [tex]\( F = m \times a \)[/tex]:
- [tex]\( F = 0.14 \text{ kg} \times 25 \text{ m/s}² \)[/tex].
- Calculate the product:
- [tex]\( F = 3.5 \text{ N} \)[/tex].
Therefore, the force needed to accelerate the ball at 25 m/s² is [tex]\( 3.5 \)[/tex] newtons.
[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).
### Step-by-Step Solution:
1. Identify the given values:
- The mass of the ball is 140 grams.
- The acceleration is 25 m/s².
2. Convert the mass to kilograms:
- Since 1 kilogram = 1000 grams, you need to convert the mass from grams to kilograms for it to align with the SI units (Standard International Units).
- [tex]\( 140 \text{ g} = \frac{140}{1000} \text{ kg} = 0.14 \text{ kg} \)[/tex].
3. Apply the formula [tex]\( F = m \times a \)[/tex]:
- [tex]\( F = 0.14 \text{ kg} \times 25 \text{ m/s}² \)[/tex].
- Calculate the product:
- [tex]\( F = 3.5 \text{ N} \)[/tex].
Therefore, the force needed to accelerate the ball at 25 m/s² is [tex]\( 3.5 \)[/tex] newtons.
