1. **State the problem:** We need to find the time it takes for a rabbit to accelerate from an initial velocity of $4.0\ \text{m/s}$ to a final velocity of $13\ \text{m/s}$ with a constant acceleration of $2.0\ \text{m/s}^2$. 2. **Formula used:** The formula relating velocity, acceleration, and time is: $$v = v_0 + at$$ where: - $v$ is the final velocity, - $v_0$ is the initial velocity, - $a$ is the acceleration, - $t$ is the time. 3. **Substitute the known values:** $$13 = 4 + 2t$$ 4. **Solve for $t$:** $$13 - 4 = 2t$$ $$9 = 2t$$ $$t = \frac{9}{2}$$ 5. **Simplify the fraction:** $$t = \frac{\cancel{9}}{\cancel{2}} = 4.5$$ 6. **Answer:** The time it takes for the rabbit to speed up from $4.0\ \text{m/s}$ to $13\ \text{m/s}$ is $4.5$ seconds.