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A ball has a mass of 140 g. What is the force needed to accelerate the ball at [tex]$25 \, \text{m/s}^2$[/tex]?

(Formula: [tex]$F = ma$[/tex])

A. 3.5 N
B. 115 N
C. 165 N
D. 4.5 N

Answer :

To find the force needed to accelerate the ball, we can use the formula [tex]\( F = m \times a \)[/tex], where [tex]\( F \)[/tex] is the force, [tex]\( m \)[/tex] is the mass, and [tex]\( a \)[/tex] is the acceleration.

Here's a step-by-step solution:

1. Identify the given values:
- Mass of the ball ([tex]\( m \)[/tex]) = 140 grams.
- Acceleration ([tex]\( a \)[/tex]) = 25 meters per second squared ([tex]\( m/s^2 \)[/tex]).

2. Convert mass from grams to kilograms:
Since 1 kilogram (kg) is equal to 1000 grams (g), convert the mass into kilograms:
[tex]\[
m_{\text{kg}} = \frac{140 \text{ g}}{1000} = 0.14 \text{ kg}
\][/tex]

3. Apply the formula for force:
Using the formula [tex]\( F = m \times a \)[/tex]:
[tex]\[
F = 0.14 \text{ kg} \times 25 \text{ m/s}^2
\][/tex]

4. Calculate the force:
[tex]\[
F = 3.5 \text{ N}
\][/tex]

Therefore, the force needed to accelerate the ball at [tex]\( 25 \text{ m/s}^2 \)[/tex] is [tex]\( 3.5 \text{ N} \)[/tex].

The correct answer is:
- 3.5 N

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