Answer :
To find the force needed to accelerate a ball with a mass of 140 grams at an acceleration of [tex]\(25 \, \text{m/s}^2\)[/tex], we can use the formula:
[tex]\[ F = ma \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( a \)[/tex] is the acceleration.
Step-by-Step Solution:
1. Convert the mass from grams to kilograms.
Since [tex]\(1 \, \text{kg} = 1000 \, \text{g}\)[/tex], you need to convert the mass of the ball from grams to kilograms:
[tex]\[
m = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg}
\][/tex]
2. Use the formula to calculate the force.
Now, substitute the mass in kilograms and the acceleration into the formula:
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2
\][/tex]
3. Calculate the result.
Perform the multiplication:
[tex]\[
F = 3.5 \, \text{N}
\][/tex]
So, the force needed to accelerate the ball is [tex]\(3.5 \, \text{N}\)[/tex]. Therefore, the correct answer is 3.5 N.
[tex]\[ F = ma \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( a \)[/tex] is the acceleration.
Step-by-Step Solution:
1. Convert the mass from grams to kilograms.
Since [tex]\(1 \, \text{kg} = 1000 \, \text{g}\)[/tex], you need to convert the mass of the ball from grams to kilograms:
[tex]\[
m = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg}
\][/tex]
2. Use the formula to calculate the force.
Now, substitute the mass in kilograms and the acceleration into the formula:
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2
\][/tex]
3. Calculate the result.
Perform the multiplication:
[tex]\[
F = 3.5 \, \text{N}
\][/tex]
So, the force needed to accelerate the ball is [tex]\(3.5 \, \text{N}\)[/tex]. Therefore, the correct answer is 3.5 N.
