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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 :

Sure! Let's solve the problem step-by-step.

We are given:
- The mass of the ball is 140 grams.
- The acceleration is [tex]\(25 \, \text{m/s}^2\)[/tex].

We need to find the force required to accelerate the ball using the formula [tex]\(F = m \times a\)[/tex], where [tex]\(F\)[/tex] is force, [tex]\(m\)[/tex] is mass, and [tex]\(a\)[/tex] is acceleration.

### Step 1: Convert Mass to Kilograms
The mass is given in grams, so we need to convert it to kilograms because the standard unit for mass in physics is kilograms.

- There are 1000 grams in 1 kilogram.
- Therefore, mass in kilograms is:
[tex]\[
\text{mass\ in\ kg} = \frac{140}{1000} = 0.14 \, \text{kg}
\][/tex]

### Step 2: Calculate the Force
Now, we use the formula [tex]\(F = m \times a\)[/tex] to calculate the force.

- Substitute the values:
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2
\][/tex]

- Calculate:
[tex]\[
F = 3.5 \, \text{N}
\][/tex]

So, the force needed to accelerate the ball is [tex]\(3.5 \, \text{N}\)[/tex].

The correct answer is [tex]\(3.5 \, \text{N}\)[/tex].

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