Answer :
To solve the problem of finding the force needed to accelerate a ball, we 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),
- [tex]\( a \)[/tex] is the acceleration in meters per second squared ([tex]\( m/s^2 \)[/tex]).
Here's a step-by-step guide:
1. Convert the Mass from Grams to Kilograms:
The mass of the ball is given as 140 grams. To convert grams to kilograms, divide by 1000:
[tex]\[
m = \frac{140 \text{ g}}{1000} = 0.14 \text{ kg}
\][/tex]
2. Use the Given Acceleration:
The acceleration is given as [tex]\( 25 \, m/s^2 \)[/tex].
3. Calculate the Force:
Apply the formula [tex]\( F = ma \)[/tex]:
[tex]\[
F = 0.14 \text{ kg} \times 25 \, m/s^2 = 3.5 \text{ N}
\][/tex]
Therefore, the force needed to accelerate the ball is 3.5 N.
- [tex]\( F \)[/tex] is the force in newtons (N),
- [tex]\( m \)[/tex] is the mass in kilograms (kg),
- [tex]\( a \)[/tex] is the acceleration in meters per second squared ([tex]\( m/s^2 \)[/tex]).
Here's a step-by-step guide:
1. Convert the Mass from Grams to Kilograms:
The mass of the ball is given as 140 grams. To convert grams to kilograms, divide by 1000:
[tex]\[
m = \frac{140 \text{ g}}{1000} = 0.14 \text{ kg}
\][/tex]
2. Use the Given Acceleration:
The acceleration is given as [tex]\( 25 \, m/s^2 \)[/tex].
3. Calculate the Force:
Apply the formula [tex]\( F = ma \)[/tex]:
[tex]\[
F = 0.14 \text{ kg} \times 25 \, m/s^2 = 3.5 \text{ N}
\][/tex]
Therefore, the force needed to accelerate the ball is 3.5 N.
