1. **State the problem:** We want to find the change in momentum, the impulse applied to the object, and the time during which the force acts. 2. **Formula for change in momentum:** The change in momentum $\Delta q$ is given by $$\Delta q = m(v - v_0)$$ where $m$ is the mass, $v_0$ is the initial velocity, and $v$ is the final velocity. 3. **Calculate change in momentum:** Given $m=4$, $v_0=5$, and $v=12$, substitute these values: $$\Delta q = 4(12 - 5) = 4 \times 7 = 28$$ So, the change in momentum is $28$ kg·m/s. 4. **Impulse:** Impulse $I$ is equal to the change in momentum: $$I = \Delta q = 28$$ Impulse has units of kg·m/s. 5. **Time of force application:** Impulse is also related to force and time by $$I = Ft$$ where $F$ is the force and $t$ is the time. 6. **Calculate time:** Given $I=28$ and $F=30$, solve for $t$: $$28 = 30t \implies t = \frac{28}{30} = 0.93$$ So, the force acts for $0.93$ seconds. **Final answers:** - Change in momentum: $28$ kg·m/s - Impulse: $28$ kg·m/s - Time of force application: $0.93$ seconds