### Graph and Question AnalysisThe graph above represents the position \( y(t) \) of a particle moving along the \( y \)-axis over time \( t \) ranging from 0 to 5. The graph has five distinct segments:1. **From \( t = 0 \) to \( t = 1 \):** The curve slopes upward, indicating positive velocity.2. **From \( t = 1 \) to \( t = 2 \):** The segment is a flat line, suggesting zero velocity.3. **From \( t = 2 \) to \( t = 3 \):** The curve slopes sharply upward, indicating increasing velocity.4. **From \( t = 3 \) to \( t = 4 \):** The curve slopes downward, indicating negative velocity.5. **From \( t = 4 \) to \( t = 5 \):** The downward slope becomes gentler, suggesting decreasing negative velocity with positive acceleration.### Question:"A particle moves along the \( y \)-axis. The graph of the particle’s position \( y(t) \) at time \( t \) is shown above for \( 0 \leq t \leq 5 \). For what values of \( t \) is the velocity of the particle negative and the acceleration positive?"#### Choices:- **A:** \( 0 < t < 1 \)- **B:** \( 1 < t < 2 \)- **C:** \( 2 < t < 3 \)- **D:** \( 3 < t < 4 \)- **E:** \( 4 < t < 5 \)**Explanation:**To determine the intervals where the velocity is negative and acceleration is positive, focus on the sections of the graph where the slope is negative (indicating negative velocity) and where the rate of change of the slope is increasing (indicating positive acceleration).- **Correct Choice: E (\( 4 < t < 5 \))**: During this interval, the particle's velocity is negative (since the curve is sloping downward), but the slope is becoming less steep, indicating positive acceleration.

Velocity is defined as slope of the graph and acceleration will be positive if velocity increases , acceleration will be negative if velocity decreases and acceleration will be zero if the velocity is constant. In t = 0 to 1 Velocity is positive constant and acceleration is 0In t = 1 to 2 Velocity is zero and acceleration is zero In t = 2 to 3 Velocity is positive and increases and acceleration is positive In t = 3 to 4 Velocity is negative constant and acceleration is zero In t = 4 to 5 Velocity is negative and increases and acceleration is positive So, the correct option is E. Answer