Answer :
To solve this problem, we need to use the formula for force, which is [tex]\( F = m \times a \)[/tex]. Here, [tex]\( F \)[/tex] is the force, [tex]\( m \)[/tex] is the mass, and [tex]\( a \)[/tex] is the acceleration.
Let's go through the steps:
1. Convert Mass to Kilograms:
The mass of the ball is given as 140 grams. We need to convert this mass into kilograms because the standard unit for mass in the formula is kilograms. To do this, we divide the mass by 1000 (since 1 kilogram = 1000 grams).
[tex]\[
m = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg}
\][/tex]
2. Identify the Acceleration:
The acceleration given is 25 meters per second squared (m/s²).
3. Apply the Formula [tex]\( F = m \times a \)[/tex]:
Now, we substitute the mass (in kg) and acceleration (in m/s²) into the formula to calculate the force.
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 = 3.5 \, \text{N}
\][/tex]
Therefore, the force needed to accelerate the ball at 25 m/s² is 3.5 Newtons.
The correct answer from the options provided is 3.5 N.
Let's go through the steps:
1. Convert Mass to Kilograms:
The mass of the ball is given as 140 grams. We need to convert this mass into kilograms because the standard unit for mass in the formula is kilograms. To do this, we divide the mass by 1000 (since 1 kilogram = 1000 grams).
[tex]\[
m = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg}
\][/tex]
2. Identify the Acceleration:
The acceleration given is 25 meters per second squared (m/s²).
3. Apply the Formula [tex]\( F = m \times a \)[/tex]:
Now, we substitute the mass (in kg) and acceleration (in m/s²) into the formula to calculate the force.
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 = 3.5 \, \text{N}
\][/tex]
Therefore, the force needed to accelerate the ball at 25 m/s² is 3.5 Newtons.
The correct answer from the options provided is 3.5 N.
