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A ball has a mass of 140 g. What is the force needed to accelerate the ball at [tex]$25 \, m/s^2$[/tex]? (Formula: [tex]$F = ma$[/tex])

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

Answer :

Sure! Let's go through the solution step-by-step.

### Question:
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]?
Given formula: [tex]\( F = ma \)[/tex]

### Step-by-Step Solution:

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

2. Convert the mass from grams to kilograms:
- Since 1 kilogram = 1000 grams, we convert the mass to kilograms:
[tex]\[
m = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg}
\][/tex]

3. Use the formula [tex]\( F = ma \)[/tex] to find the force:
- Here, [tex]\( m = 0.14 \, \text{kg} \)[/tex] and [tex]\( a = 25 \, \text{m/s}^2 \)[/tex].
- Substitute these values into the formula:
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2 = 3.5 \, \text{N}
\][/tex]

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

### Correct Answer:
- 3.5 N

This detailed explanation matches with the computational result, showing that the correct answer is 3.5 N.

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