Advanced Level Mechanics Revision: Kinematics & Equilibrium

Mastering Advanced Level Mechanics requires a strong command of vector calculus for kinematics, variable work-energy integrations, and structural static equilibrium systems. Test your problem-solving skills with these detailed structured problems from image_3539f5.jpg (also referenced as image_353cdf.jpg).

1. Vector Kinematics & Particle Dynamics

Question 1

• (i) The position vector r of a particle P of mass 2 kg at time t seconds is given by:

  r = [4ti + t^3*j + (1/2)t^2k] m

  Tasks:

  • (a) Find the velocity and the acceleration vectors of P when t = 2. (4 marks)

  • (b) Find the work done by P in the time interval 1 <= t <= 2. (3 marks)

2. Coplanar Force Systems & Static Equilibrium

• (ii) Forces F1 and F2 act at points with position vectors r1 and r2 respectively, where:

  F1 = (ai + 3j) N, r1 = (2i – j) m F2 = (-bi – 4j) N, r2 = (5i + 3j) m

  Tasks:

  • (c) State the two conditions necessary for a system of coplanar forces to be in static equilibrium. (2 marks)

  • (d) Given that the system of forces is in equilibrium, find the values of the constants a and b. (4 marks)

3. Center of Gravity & Rigid Body Mechanics

Question 2

• (i) A uniform square lamina ABCD has sides of length 4 cm. A triangle BCE with an altitude EF = 3 cm, where F is the midpoint of side BC, is cut off and removed from the square (as shown in Figure 2 of image_3539f5.jpg). Find the distance of the center of gravity of the remaining composite lamina ABERD from the baseline side AD. (7 marks)

4. Rectilinear Motion & Variable Velocity Profiles

Question 3

• (i) A train travels along a straight horizontal road between two stations A and B which are 6300 m apart. The train starts from rest at station A and moves with a constant acceleration of 0.5 m s^-2 until it reaches a maximum speed v m s^-1 (where v < 50). The train then maintains this uniform speed v for a time duration t, and subsequently decelerates uniformly at 0.25 m s^-2 until coming to rest at station B. The total time elapsed for the entire journey is 300 s.

  Tasks:

  • (a) Find an expression for t in terms of v. (3 marks)

  • (b) Calculate the absolute value of v. (4 marks)

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