Answer :
Sure! Let's work through the problem step-by-step to find the force needed to accelerate the ball.
1. Understand the given values:
- Mass of the ball ([tex]\( m \)[/tex]) = 140 grams
- Acceleration ([tex]\( a \)[/tex]) = 25 [tex]\( \text{m/s}^2 \)[/tex]
2. Convert the mass from grams to kilograms:
Since there are 1000 grams in a kilogram, we need to convert 140 grams to kilograms.
[tex]\[
\text{Mass in kilograms} = \frac{140 \text{ grams}}{1000} = 0.14 \text{ kg}
\][/tex]
3. Use the formula for force:
The formula to calculate force is given by [tex]\( F = m \times a \)[/tex], where:
- [tex]\( F \)[/tex] is the force
- [tex]\( m \)[/tex] is the mass
- [tex]\( a \)[/tex] is the acceleration
4. Substitute the values into the formula:
[tex]\[
F = 0.14 \text{ kg} \times 25 \text{ m/s}^2
\][/tex]
5. Calculate the force:
[tex]\[
F = 3.5 \text{ Newtons}
\][/tex]
So, the force needed to accelerate the ball at 25 [tex]\( \text{m/s}^2 \)[/tex] is [tex]\(\boxed{3.5 \text{ N}}\)[/tex].
The correct answer from the given options is 3.5 N.
1. Understand the given values:
- Mass of the ball ([tex]\( m \)[/tex]) = 140 grams
- Acceleration ([tex]\( a \)[/tex]) = 25 [tex]\( \text{m/s}^2 \)[/tex]
2. Convert the mass from grams to kilograms:
Since there are 1000 grams in a kilogram, we need to convert 140 grams to kilograms.
[tex]\[
\text{Mass in kilograms} = \frac{140 \text{ grams}}{1000} = 0.14 \text{ kg}
\][/tex]
3. Use the formula for force:
The formula to calculate force is given by [tex]\( F = m \times a \)[/tex], where:
- [tex]\( F \)[/tex] is the force
- [tex]\( m \)[/tex] is the mass
- [tex]\( a \)[/tex] is the acceleration
4. Substitute the values into the formula:
[tex]\[
F = 0.14 \text{ kg} \times 25 \text{ m/s}^2
\][/tex]
5. Calculate the force:
[tex]\[
F = 3.5 \text{ Newtons}
\][/tex]
So, the force needed to accelerate the ball at 25 [tex]\( \text{m/s}^2 \)[/tex] is [tex]\(\boxed{3.5 \text{ N}}\)[/tex].
The correct answer from the given options is 3.5 N.
