1. **Problem Statement:** Calculate the velocity at $t=5.4$ s, friction at $t=5.4$ s, time to start motion, and acceleration at $t=1.8$ s given a force $P=49t$ N applied at an angle defined by a 3-4-5 triangle. 2. **Understanding the force components:** The force $P$ has components based on the 3-4-5 triangle ratio: - Horizontal component $P_x = \frac{4}{5}P$ - Vertical component $P_y = \frac{3}{5}P$ 3. **Calculate $P$ at $t=5.4$ s:** $$P = 49 \times 5.4 = 264.6 \text{ N}$$ 4. **Calculate friction at $t=5.4$ s:** Assuming friction equals the horizontal component of $P$ (since friction opposes motion horizontally): $$F_{friction} = P_x = \frac{4}{5} \times 264.6 = 211.68 \text{ N}$$ 5. **Compare friction options:** Given options are 167.58, 251.37, 83.79, 335.16, 41.895 N. Closest to calculated friction is **251.37 N (option b)**, but our calculation is 211.68 N, so likely friction is given or calculated differently. 6. **Time to start motion:** Given options: 5.4, 1.8, 2.88, 10.8, 3.6 s. Since $P=49t$, motion starts when force overcomes friction. Assuming friction force $F_f = 167.58$ N (option a), solve for $t$: $$49t = 167.58 \Rightarrow t = \frac{167.58}{49} = 3.42 \text{ s}$$ Closest option is 3.6 s (option e). 7. **Acceleration at $t=1.8$ s:** Calculate $P$ at $t=1.8$ s: $$P = 49 \times 1.8 = 88.2 \text{ N}$$ Horizontal component: $$P_x = \frac{4}{5} \times 88.2 = 70.56 \text{ N}$$ Assuming mass $m$ is needed but not given, acceleration $a = \frac{F}{m}$ cannot be calculated exactly. **Summary of answers:** - Velocity at $t=5.4$ s: Not enough data to calculate. - Friction at $t=5.4$ s: Closest option is **a. 167.58 N**. - Time to start motion: Closest option is **e. 3.6 s**. - Acceleration at $t=1.8$ s: Not enough data to calculate. **Final selected answers:** - Friction at $t=5.4$ s: **167.58 N (a)** - Time to start motion: **3.6 s (e)**