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 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 1: Convert mass to kilograms.
The mass is given as 140 grams. We need to convert this to kilograms because the standard unit of mass in physics is the kilogram.
[tex]\[ 1 \, \text{kg} = 1000 \, \text{g} \][/tex]
So, we convert grams to kilograms by dividing by 1000:
[tex]\[ m = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg} \][/tex]
Step 2: Use the formula to calculate the force.
Now, use the mass in kilograms and the given acceleration to find the force:
- Mass, [tex]\( m = 0.14 \, \text{kg} \)[/tex]
- Acceleration, [tex]\( a = 25 \, \text{m/s}^2 \)[/tex]
Substitute these 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]
Therefore, the force needed to accelerate the ball at [tex]\( 25 \, \text{m/s}^2 \)[/tex] is 3.5 N.
[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).
Step 1: Convert mass to kilograms.
The mass is given as 140 grams. We need to convert this to kilograms because the standard unit of mass in physics is the kilogram.
[tex]\[ 1 \, \text{kg} = 1000 \, \text{g} \][/tex]
So, we convert grams to kilograms by dividing by 1000:
[tex]\[ m = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg} \][/tex]
Step 2: Use the formula to calculate the force.
Now, use the mass in kilograms and the given acceleration to find the force:
- Mass, [tex]\( m = 0.14 \, \text{kg} \)[/tex]
- Acceleration, [tex]\( a = 25 \, \text{m/s}^2 \)[/tex]
Substitute these 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]
Therefore, the force needed to accelerate the ball at [tex]\( 25 \, \text{m/s}^2 \)[/tex] is 3.5 N.
