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A boy rolls a 200 g basketball horizontally on the floor with a net force of 2 N to the right. What is the acceleration of the basketball?

Given:
[tex]\[ m = 200 \, \text{g} \][/tex]
[tex]\[ \vec{F} = 2 \, \text{N} \][/tex]

Find the acceleration [tex]\(\vec{a}\)[/tex].

Sagot :

GinnyAnsweridn
Sure, let's solve this problem step-by-step.

### Step 1: Understand the Given Values
- Mass of the basketball (m): 200 grams
- Net force acting on the basketball (F): 2 Newtons

### Step 2: Convert Mass to Kilograms
Mass is usually given in grams but for calculations involving Newton's second law, it's appropriate to convert it to kilograms.
- 1 kilogram (kg) = 1000 grams (g)
- Therefore, Mass (m) in kilograms = [tex]\(\frac{200 \text{ g}}{1000} = 0.2 \text{ kg}\)[/tex]

### Step 3: Apply Newton's Second Law of Motion
Newton's second law states that:
[tex]\[ \vec{F} = m \vec{a} \][/tex]
Where:
- [tex]\(\vec{F}\)[/tex] is the net force
- [tex]\(m\)[/tex] is the mass
- [tex]\(\vec{a}\)[/tex] is the acceleration

Rewriting this for acceleration ([tex]\(\vec{a}\)[/tex]):
[tex]\[ \vec{a} = \frac{\vec{F}}{m} \][/tex]

### Step 4: Substitute the Given Values into the Formula
Now, substitute the net force (F) and the mass (m) into the formula to find the acceleration.
[tex]\[ \vec{a} = \frac{2 \text{ N}}{0.2 \text{ kg}} \][/tex]

### Step 5: Calculate the Acceleration
[tex]\[ \vec{a} = \frac{2}{0.2} = 10 \text{ m/s}^2 \][/tex]

### Conclusion
The acceleration of the basketball is [tex]\(10 \text{ m/s}^2\)[/tex] directed to the right.
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