1. The problem asks to create a graphic where acceleration $a_x$ is the dependent variable and time $t$ is the independent variable, based on the given velocity-time graph. 2. Recall that acceleration is the rate of change of velocity with respect to time, mathematically expressed as: $$a_x = \frac{\Delta v_x}{\Delta t}$$ 3. We analyze the velocity graph in segments to find acceleration in each interval: - From $t=0$ to $t=2$ seconds, velocity decreases from 0 to -4 m/s. $$a_x = \frac{-4 - 0}{2 - 0} = \frac{-4}{2} = -2 \text{ m/s}^2$$ - From $t=2$ to $t=4$ seconds, velocity increases from -4 to 4 m/s. $$a_x = \frac{4 - (-4)}{4 - 2} = \frac{8}{2} = 4 \text{ m/s}^2$$ - From $t=4$ to $t=6$ seconds, velocity remains constant at 4 m/s. $$a_x = \frac{4 - 4}{6 - 4} = \frac{0}{2} = 0 \text{ m/s}^2$$ 4. The acceleration-time graph is therefore piecewise constant with values: - $a_x = -2$ m/s$^2$ for $0 \leq t < 2$ - $a_x = 4$ m/s$^2$ for $2 \leq t < 4$ - $a_x = 0$ m/s$^2$ for $4 \leq t \leq 6$ 5. This graph can be represented as a step function with these values over the respective time intervals.