Answer :
Sure! Let's find the force needed to accelerate the ball.
1. Understand the Problem:
We have a ball with a mass of 140 grams and we want to accelerate it at a rate of [tex]\(25 \, \text{m/s}^2\)[/tex]. We need to find the force in newtons.
2. Convert the Mass to Kilograms:
The mass of the ball is given in grams, but we need it in kilograms to use in the formula. Since 1 kilogram is 1000 grams, we convert the mass as follows:
[tex]\[
140 \, \text{g} = \frac{140}{1000} \, \text{kg} = 0.14 \, \text{kg}
\][/tex]
3. Use the Formula for Force:
To find the force ([tex]\(F\)[/tex]), we will use the formula:
[tex]\[
F = m \cdot a
\][/tex]
where [tex]\(m\)[/tex] is the mass and [tex]\(a\)[/tex] is the acceleration. We have:
- [tex]\(m = 0.14 \, \text{kg}\)[/tex]
- [tex]\(a = 25 \, \text{m/s}^2\)[/tex]
4. Calculate the Force:
Now we can plug the values into the formula to get:
[tex]\[
F = 0.14 \times 25 = 3.5 \, \text{N}
\][/tex]
5. Conclusion:
The force needed to accelerate the ball at [tex]\(25 \, \text{m/s}^2\)[/tex] is [tex]\(3.5 \, \text{N}\)[/tex].
So, the correct answer is [tex]\(3.5 \, \text{N}\)[/tex].
1. Understand the Problem:
We have a ball with a mass of 140 grams and we want to accelerate it at a rate of [tex]\(25 \, \text{m/s}^2\)[/tex]. We need to find the force in newtons.
2. Convert the Mass to Kilograms:
The mass of the ball is given in grams, but we need it in kilograms to use in the formula. Since 1 kilogram is 1000 grams, we convert the mass as follows:
[tex]\[
140 \, \text{g} = \frac{140}{1000} \, \text{kg} = 0.14 \, \text{kg}
\][/tex]
3. Use the Formula for Force:
To find the force ([tex]\(F\)[/tex]), we will use the formula:
[tex]\[
F = m \cdot a
\][/tex]
where [tex]\(m\)[/tex] is the mass and [tex]\(a\)[/tex] is the acceleration. We have:
- [tex]\(m = 0.14 \, \text{kg}\)[/tex]
- [tex]\(a = 25 \, \text{m/s}^2\)[/tex]
4. Calculate the Force:
Now we can plug the values into the formula to get:
[tex]\[
F = 0.14 \times 25 = 3.5 \, \text{N}
\][/tex]
5. Conclusion:
The force needed to accelerate the ball at [tex]\(25 \, \text{m/s}^2\)[/tex] is [tex]\(3.5 \, \text{N}\)[/tex].
So, the correct answer is [tex]\(3.5 \, \text{N}\)[/tex].
