Answer :
To find the force needed to accelerate a ball, we can 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), and [tex]\( a \)[/tex] is the acceleration in meters per second squared (m/s²).
Here's how you can solve the problem step-by-step:
1. Convert the mass from grams to kilograms:
- The mass of the ball is given as 140 grams.
- Since there are 1000 grams in a kilogram, you divide the mass by 1000 to convert it to kilograms.
[tex]\[
m = \frac{140 \text{ g}}{1000} = 0.14 \text{ kg}
\][/tex]
2. Use the formula to calculate the force:
- Given that the acceleration [tex]\( a = 25 \, \text{m/s}^2 \)[/tex].
- Substitute the mass [tex]\( m = 0.14 \, \text{kg} \)[/tex] and the acceleration [tex]\( a = 25 \, \text{m/s}^2 \)[/tex] into the formula:
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2
\][/tex]
3. Calculate the force:
- Perform the multiplication:
[tex]\[
F = 3.5 \, \text{N}
\][/tex]
Therefore, the force needed to accelerate the ball is [tex]\( 3.5 \, \text{N} \)[/tex].
[tex]\[ F = ma \][/tex]
where [tex]\( F \)[/tex] is the force in newtons (N), [tex]\( m \)[/tex] is the mass in kilograms (kg), and [tex]\( a \)[/tex] is the acceleration in meters per second squared (m/s²).
Here's how you can solve the problem step-by-step:
1. Convert the mass from grams to kilograms:
- The mass of the ball is given as 140 grams.
- Since there are 1000 grams in a kilogram, you divide the mass by 1000 to convert it to kilograms.
[tex]\[
m = \frac{140 \text{ g}}{1000} = 0.14 \text{ kg}
\][/tex]
2. Use the formula to calculate the force:
- Given that the acceleration [tex]\( a = 25 \, \text{m/s}^2 \)[/tex].
- Substitute the mass [tex]\( m = 0.14 \, \text{kg} \)[/tex] and the acceleration [tex]\( a = 25 \, \text{m/s}^2 \)[/tex] into the formula:
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2
\][/tex]
3. Calculate the force:
- Perform the multiplication:
[tex]\[
F = 3.5 \, \text{N}
\][/tex]
Therefore, the force needed to accelerate the ball is [tex]\( 3.5 \, \text{N} \)[/tex].
