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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 solve this problem, we need to find the force required to accelerate a ball with a given mass. The formula to use is [tex]\( F = ma \)[/tex], where [tex]\( F \)[/tex] is the force, [tex]\( m \)[/tex] is the mass in kilograms, and [tex]\( a \)[/tex] is the acceleration.

Here are the steps to solve the problem:

1. Identify the given values:
- Mass of the ball = 140 grams
- Acceleration = [tex]\( 25 \, \text{m/s}^2 \)[/tex]

2. Convert the mass from grams to kilograms:
To work with the SI unit system, we need the mass in kilograms. We know that 1 kilogram equals 1000 grams. So, we convert 140 grams to kilograms:
[tex]\[
\text{mass in kg} = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg}
\][/tex]

3. Apply the formula [tex]\( F = ma \)[/tex]:
Using the mass in kilograms and the given acceleration, we calculate the force:
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 = 3.5 \, \text{N}
\][/tex]

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

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