4. A biker is accelerating when she applies the brakes and then speeds up again. The net horizontal force is shown in the graph. Assume she moves in a straight line and the mass of the biker and bike is 80 kg. The biker was moving at 8 m/s at t = 0. How fast is she moving at t = 20 s? net x-Force (Newtons) 40 20 400 4 8 12 time (sec) 16 20
4. A biker is accelerating when she applies the brakes and then speeds up again. The net horizontal force is shown in the graph. Assume she moves in a straight line and the mass of the biker and bike is 80 kg. The biker was moving at 8 m/s at t = 0. How fast is she moving at t = 20 s? net x-Force (Newtons) 40 20 400 4 8 12 time (sec) 16 20
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Hi, I need help with number 4, thank you
![### Problem Statement
A biker is accelerating when she applies the brakes and then speeds up again. The net horizontal force is shown in the graph. Assume she moves in a straight line and the mass of the biker and bike is 80 kg. The biker was moving at 8 m/s at \( t = 0 \). How fast is she moving at \( t = 20 \, \text{s} \)?
### Graph Description
The graph represents the net horizontal force applied on the biker over time.
- On the y-axis, the net x-Force is measured in Newtons (N), with values ranging from -40 N to 40 N.
- On the x-axis, time is measured in seconds (sec), ranging from 0 to 20 seconds.
#### Graph Details:
1. From \( t = 0 \, \text{s} \) to \( t = 8 \, \text{s} \), the net x-Force is constant at 20 N.
2. At \( t = 8 \, \text{s} \), the net x-Force drops sharply to -20 N and remains constant until \( t = 12 \, \text{s} \).
3. From \( t = 12 \, \text{s} \) to \( t = 16 \, \text{s} \), the net x-Force increases linearly from -20 N to 10 N.
4. From \( t = 16 \, \text{s} \) to \( t = 20 \, \text{s} \), the net x-Force remains constant at 10 N.
### Solution Steps
1. **Calculation of Acceleration and Velocity:**
- Use Newton's second law, \( F = ma \), to find acceleration for each time interval.
2. **First Interval (0 to 8 seconds):**
- Force \( F = 20 \, \text{N} \)
- Mass \( m = 80 \, \text{kg} \)
- Acceleration \( a = \frac{F}{m} = \frac{20}{80} = 0.25 \, \text{m/s}^2 \)
Velocity at \( t = 8 \, \text{s} \):
\[ V_1 = V_0 + at = 8 + 0.25 \times](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5d4e29f-131d-4c29-ab80-9c0dd009bcff%2F0e5e96c8-12ee-4f1a-aec5-79b21e6b8b4d%2Fbu0w5el_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
A biker is accelerating when she applies the brakes and then speeds up again. The net horizontal force is shown in the graph. Assume she moves in a straight line and the mass of the biker and bike is 80 kg. The biker was moving at 8 m/s at \( t = 0 \). How fast is she moving at \( t = 20 \, \text{s} \)?
### Graph Description
The graph represents the net horizontal force applied on the biker over time.
- On the y-axis, the net x-Force is measured in Newtons (N), with values ranging from -40 N to 40 N.
- On the x-axis, time is measured in seconds (sec), ranging from 0 to 20 seconds.
#### Graph Details:
1. From \( t = 0 \, \text{s} \) to \( t = 8 \, \text{s} \), the net x-Force is constant at 20 N.
2. At \( t = 8 \, \text{s} \), the net x-Force drops sharply to -20 N and remains constant until \( t = 12 \, \text{s} \).
3. From \( t = 12 \, \text{s} \) to \( t = 16 \, \text{s} \), the net x-Force increases linearly from -20 N to 10 N.
4. From \( t = 16 \, \text{s} \) to \( t = 20 \, \text{s} \), the net x-Force remains constant at 10 N.
### Solution Steps
1. **Calculation of Acceleration and Velocity:**
- Use Newton's second law, \( F = ma \), to find acceleration for each time interval.
2. **First Interval (0 to 8 seconds):**
- Force \( F = 20 \, \text{N} \)
- Mass \( m = 80 \, \text{kg} \)
- Acceleration \( a = \frac{F}{m} = \frac{20}{80} = 0.25 \, \text{m/s}^2 \)
Velocity at \( t = 8 \, \text{s} \):
\[ V_1 = V_0 + at = 8 + 0.25 \times
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