Question 1: (5 Marks) A particle moves along a straight line with a velocity given by (t) = 51 - 4t+2. where v(t) is

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Question 1: (5 Marks) A particle moves along a straight line with a velocity given by (t) = 51 - 4t+2. where v(t) is in meters per second and f is in seconds (a) Determine the acceleration of the particle at t = 3 seconds. (2 Marks) (b) Calculate the displacement of the particle between t = 2 seconds and t seconds. (3 Marks) Question 2: (4 Marks) A mass m is attached to a spring with a spring constant & 100 N/m and oscillates with simple harmonic motion. If the amplitude of oscillation is 0.1 m, determine: (a) The angular frequency of the oscillation. (2 Marks) (b) The total energy of the system. (2 Marks) Question 3: (3 Marks) A block of mass 2 kg is placed on a frictionless inclined plane making an angle of 30" with the horizontal. Calculate (a) The acceleration of the block down the plane. (2 Marks) (b) The time it takes for the block to slide 4 meters down the plane. (1 Mark) Question 4: (3 Marks) Two objects with masses m = 4 kg and m = 6 kg are moving towards each other on a frictionless surface with velocities =3m/s and 2-2 m/s respectively. Assuming a perfectly elastic collision, find: (a) The final velocity of each mass after the collision. (2 Marks) (b) The total kinetic energy before and after the collision. (1 Mark)