Answer :
To find the force needed to accelerate the ball, we can use the formula [tex]\( F = ma \)[/tex], where [tex]\( F \)[/tex] is the force in newtons, [tex]\( m \)[/tex] is the mass in kilograms, and [tex]\( a \)[/tex] is the acceleration in meters per second squared.
Here's how you can solve the problem step-by-step:
1. Convert the mass to kilograms:
The mass provided is 140 grams. To convert grams to kilograms, you divide by 1,000 (since 1 kilogram = 1,000 grams).
[tex]\[
m = \frac{140 \text{ g}}{1000} = 0.14 \text{ kg}
\][/tex]
2. Use the formula [tex]\( F = ma \)[/tex]:
Now that we have the mass in kilograms, we can use the formula for force. The acceleration is given as [tex]\( 25 \, \text{m/s}^2 \)[/tex].
[tex]\[
F = 0.14 \text{ kg} \times 25 \text{ m/s}^2
\][/tex]
3. Calculate the force:
Multiply the mass ([tex]\( 0.14 \, \text{kg} \)[/tex]) by the acceleration ([tex]\( 25 \, \text{m/s}^2 \)[/tex]).
[tex]\[
F = 3.5 \, \text{N}
\][/tex]
Therefore, the force needed to accelerate the ball is [tex]\( 3.5 \, \text{N} \)[/tex].
Here's how you can solve the problem step-by-step:
1. Convert the mass to kilograms:
The mass provided is 140 grams. To convert grams to kilograms, you divide by 1,000 (since 1 kilogram = 1,000 grams).
[tex]\[
m = \frac{140 \text{ g}}{1000} = 0.14 \text{ kg}
\][/tex]
2. Use the formula [tex]\( F = ma \)[/tex]:
Now that we have the mass in kilograms, we can use the formula for force. The acceleration is given as [tex]\( 25 \, \text{m/s}^2 \)[/tex].
[tex]\[
F = 0.14 \text{ kg} \times 25 \text{ m/s}^2
\][/tex]
3. Calculate the force:
Multiply the mass ([tex]\( 0.14 \, \text{kg} \)[/tex]) by the acceleration ([tex]\( 25 \, \text{m/s}^2 \)[/tex]).
[tex]\[
F = 3.5 \, \text{N}
\][/tex]
Therefore, the force needed to accelerate the ball is [tex]\( 3.5 \, \text{N} \)[/tex].
