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,
- [tex]\( m \)[/tex] is the mass, and
- [tex]\( a \)[/tex] is the acceleration.
Here's how you can solve it step-by-step:
1. Convert the mass to kilograms:
The mass of the ball is given as 140 grams. To use the formula, we need the mass in kilograms.
Since 1 kilogram = 1000 grams, we convert the mass by dividing by 1000:
[tex]\[ m = \frac{140}{1000} = 0.14 \text{ kg} \][/tex]
2. Use the formula to find the force:
The acceleration [tex]\( a \)[/tex] is given as 25 m/s².
Plug the values into the formula:
[tex]\[ F = 0.14 \times 25 \][/tex]
3. Calculate the force:
[tex]\[ F = 3.5 \text{ N} \][/tex]
So, the force needed to accelerate the ball at 25 m/s² is [tex]\( 3.5 \text{ N} \)[/tex].
[tex]\[ F = ma \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass, and
- [tex]\( a \)[/tex] is the acceleration.
Here's how you can solve it step-by-step:
1. Convert the mass to kilograms:
The mass of the ball is given as 140 grams. To use the formula, we need the mass in kilograms.
Since 1 kilogram = 1000 grams, we convert the mass by dividing by 1000:
[tex]\[ m = \frac{140}{1000} = 0.14 \text{ kg} \][/tex]
2. Use the formula to find the force:
The acceleration [tex]\( a \)[/tex] is given as 25 m/s².
Plug the values into the formula:
[tex]\[ F = 0.14 \times 25 \][/tex]
3. Calculate the force:
[tex]\[ F = 3.5 \text{ N} \][/tex]
So, the force needed to accelerate the ball at 25 m/s² is [tex]\( 3.5 \text{ N} \)[/tex].
