https://r2.erweima.ai/mathbot/image/1726188216944zrly16cy.jpg

### Graphs:
1. **Velocity-Time \(v(t)\) Graph**:
   - The velocity increases linearly from 0 to 30 m/s between \( t = 0 \) and \( t = 20 \) seconds.
   - It remains constant at 30 m/s from \( t = 20 \) to \( t = 30 \) seconds.
   - It decreases linearly to 0 m/s between \( t = 30 \) and \( t = 50 \) seconds.

2. **Acceleration-Time \(a(t)\) Graph**:
   - The acceleration is \( 1.5 \, \text{m/s}^2 \) from \( t = 0 \) to \( t = 20 \) seconds.
   - The acceleration is \( 0 \, \text{m/s}^2 \) from \( t = 20 \) to \( t = 30 \) seconds.
   - The acceleration is \( -1.5 \, \text{m/s}^2 \) from \( t = 30 \) to \( t = 50 \) seconds.

3. **Position-Time \(x(t)\) Graph**:
   - The position increases quadratically during the first phase (0 to 20 seconds).
   - It increases linearly during the second phase (20 to 30 seconds).
   - It continues to increase but at a decreasing rate during the last phase (30 to 50 seconds).

### Questions:
1. Would you like a detailed explanation of how these graphs were derived?
2. Do you need the calculations for specific points on the \( x(t) \) graph?
3. Should we analyze the maximum distance traveled?
4. Would you like to calculate the total distance covered?
5. Do you want to discuss the physical interpretation of the acceleration and its impact on motion?

**Tip:** Always cross-check the units and their consistency when analyzing or solving physics problems involving motion.

La gráfica de la figura representa la velocidad en función del tiempo de un móvil que sale del origen de coordenadas y sigue un movimiento rectilíneo. Calcula: a) Dibuja la gráfica x(t) y a(t) b) ¿Cuál es la aceleración del móvil en el instante t = 20 s? c) ¿Cuál es la distancia recorrida durante el movimiento de frenada? d) ¿En qué intervalo de tiempo la aceleración es máximo?

Solve the physics problem involving velocity-time graph analysis for a moving object in rectilinear motion. Learn to draw position-time and acceleration-time graphs, calculate acceleration at a specific time, determine the distance during braking, and find when acceleration is maximum. Suitable for high school students (Grades 9-12).

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