1. **Problem Statement:** For Q1, we need to identify which velocity-versus-time graph corresponds to the given acceleration-versus-time graph where acceleration is zero initially, then negative for a short time, then zero again. The particle initially moves to the right (positive velocity). 2. **Understanding the relationship between acceleration and velocity:** Acceleration is the rate of change of velocity: $$a_x = \frac{dv_x}{dt}$$ - When acceleration is zero, velocity is constant. - When acceleration is negative, velocity decreases. 3. **Analyzing the acceleration graph:** - Initially, $a_x=0$, so velocity is constant and positive. - Then $a_x<0$ for a short interval, so velocity decreases during this time. - Finally, $a_x=0$ again, so velocity becomes constant again at a lower value. 4. **Matching velocity graphs:** - Graph (a) shows velocity constant, then two step decreases, then constant. - Graph (b) shows velocity constant, then a longer plateau at a lower velocity, then another decrease. - Graph (c) shows a gradual decrease in velocity in two steps. - Graph (d) shows velocity increasing in steps, which contradicts negative acceleration. 5. **Conclusion:** The acceleration graph implies velocity should be constant, then decrease, then constant again. Graph (a) matches this behavior best because it shows velocity constant, then two step decreases, then constant. **Final answer:** The velocity graph that matches the acceleration graph is graph (a).