Let's solve the problem step-by-step:
### Step 1: Understanding the given data
- Initial velocity ([tex]$v_{initial}$[/tex]) = 20 m/s
- Final velocity ([tex]$v_{final}$[/tex]) = 0 m/s
- Time ([tex]$t$[/tex]) = 2 seconds
- Mass of the ball ([tex]$m$[/tex]) = 1 kg (assumed)
### Step 2: Calculate the acceleration
To find the acceleration, we use the following formula from kinematics:
[tex]\[ a = \frac{v_{final} - v_{initial}}{t} \][/tex]
Substituting the given values:
[tex]\[ a = \frac{0 \, \text{m/s} - 20 \, \text{m/s}}{2 \, \text{s}} \][/tex]
[tex]\[ a = \frac{-20 \, \text{m/s}}{2 \, \text{s}} \][/tex]
[tex]\[ a = -10 \, \text{m/s}^2 \][/tex]
So, the acceleration is [tex]\(-10 \, \text{m/s}^2\)[/tex].
### Step 3: Calculate the force applied
To find the force, we can use Newton's second law of motion, which states:
[tex]\[ F = m \cdot a \][/tex]
where [tex]\( F \)[/tex] is the force, [tex]\( m \)[/tex] is the mass, and [tex]\( a \)[/tex] is the acceleration.
Given:
- Mass ([tex]\( m \)[/tex]) = 1 kg
- Acceleration ([tex]\( a \)[/tex]) = -10 m/s²
Substituting these values into the formula:
[tex]\[ F = 1 \, \text{kg} \cdot (-10 \, \text{m/s}^2) \][/tex]
[tex]\[ F = -10 \, \text{N} \][/tex]
So, the force applied is [tex]\(-10 \, \text{N}\)[/tex].
### Step 4: Convert the force to fectonewtons
1 fectonewton (fN) = [tex]\(10^{15}\)[/tex] newtons (N).
To convert the force from newtons to fectonewtons:
[tex]\[ \text{Force in fN} = \text{Force in N} \times 10^{15} \][/tex]
[tex]\[ \text{Force in fN} = -10 \, \text{N} \times 10^{15} \][/tex]
[tex]\[ \text{Force in fN} = -1 \times 10^{16} \, \text{fN} \][/tex]
### Summary
1. Acceleration of the ball: [tex]\(-10 \, \text{m/s}^2\)[/tex]
2. Force applied by the ball: [tex]\(-10 \, \text{N}\)[/tex]
3. Force in fectonewtons: [tex]\(-1 \times 10^{16} \, \text{fN}\)[/tex]
Thus, we have successfully solved the problem step by step, finding the force applied by the ball in fectonewtons.
