A student is pulling their dog in a wagon. The velocity of the dog and wagon system is shown in the t(mathrm(~s)) & v(mathrm(~m) / mathrm(s)) 0 & 1 1 & 1.5 2 & 2 3 & 2.5 4 & 3 Which of the following are true about the energy of the dog-wagon system? Select all that apply. Positive work is being done on the system. B. Negative work is being done on the system. C. The kinetic energy of the system is constant. D. The kinetic energy of the system is decreasirg E. The kinetic energy of the system is increasing.

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A student is pulling their dog in a wagon. The velocity of the dog and wagon system is shown in the t(mathrm(~s)) & v(mathrm(~m) / mathrm(s)) 0 & 1 1 & 1.5 2 & 2 3 & 2.5 4 & 3 Which of the following are true about the energy of the dog-wagon system? Select all that apply. Positive work is being done on the system. B. Negative work is being done on the system. C. The kinetic energy of the system is constant. D. The kinetic energy of the system is decreasirg E. The kinetic energy of the system is increasing.

Answer 1

# Explanation To determine which of the statements about the energy of the dog-wagon system are true, we need to analyze the given data and understand the concepts of work and kinetic energy. ### Step-by-Step Analysis: 1. **Velocity Analysis:** The table provides the velocity \( v \) of the dog-wagon system at different times \( t \): \[ \begin{array}{|c|c|} \hline t (\text{s}) & v (\text{m/s}) \\ \hline 0 & 1 \\ \hline 1 & 1.5 \\ \hline 2 & 2 \\ \hline 3 & 2.5 \\ \hline 4 & 3 \\ \hline \end{array} \] 2. **Kinetic Energy Calculation:** The kinetic energy \( K \) of an object is given by the formula: \[ K = \frac{1}{2} m v^2 \] where \( m \) is the mass of the system and \( v \) is the velocity. Since the mass \( m \) of the system is constant, the kinetic energy \( K \) is directly proportional to the square of the velocity \( v \). 3. **Trend in Velocity:** Observing the table, we see that the velocity \( v \) is increasing with time \( t \): \[ v(0) = 1 \, \text{m/s}, \quad v(1) = 1.5 \, \text{m/s}, \quad v(2) = 2 \, \text{m/s}, \quad v(3) = 2.5 \, \text{m/s}, \quad v(4) = 3 \, \text{m/s} \] 4. **Kinetic Energy Trend:** Since the velocity is increasing, the kinetic energy \( K \) of the system is also increasing over time. 5. **Work Done:** Work \( W \) is related to the change in kinetic energy: \[ W = \Delta K \] Since the kinetic energy is increasing, positive work is being done on the system. ### Evaluation of Statements: - **A. Positive work is being done on the system.** - True, because the kinetic energy is increasing. - **B. Negative work is being done on the system.** - False, because negative work would imply a decrease in kinetic energy. - **C. The kinetic energy of the system is constant.** - False, because the kinetic energy is increasing. - **D. The kinetic energy of the system is decreasing.** - False, because the kinetic energy is increasing. - **E. The kinetic energy of the system is increasing.** - True, because the velocity is increasing, leading to an increase in kinetic energy. # Answer A. Positive work is being done on the system. E. The kinetic energy of the system is increasing.

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