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QUESTION 14 (4 marks) The motion of an object that moves in a straight line is given by v(x) —cos ! (2x) where v 1s the velocity (m s™!) and x is the displacement (m) from the origin. a) Determine a(x) where a is the acceleration (m s2) of the object. [2 marks] b) Use the result from 14a) to determine a(0) given —2rn < a(0) < 0. Express your answer in simplest form. [2 marks]
QUESTION 1 The position x (m) at time 7 (s) of a 7 kg particle moving in a straight line is given by x=3 —5 +2t—4 for 0 <1 <10 Determine the time when the particle has a momentum of 620 kg m s . A) 173s (B) 2.60s (C) 3.66s (D) 371s
QUESTION 4 D . o . . . . Tt A particle is moving with simple harmonic motion described by the equation x =1.32 cos[;} where x (m) is the displacement of the particle from a central position over time ¢ (s) t>0 The maximum speed of the particle is (A) 2.07ms! (B) 4.15m 5! (C) 430ms™! (D) 5.28 m 5!
QUESTION 17 (7 marks) An object is released from rest at a height of 100 m above the ground. The motion of the vertical descent of the object is modelled by v 9 810 004 (v>0) dx where v is the velocity (m s) and x is the displacement from the ground (m). Determine the velocity of the object when it strikes the ground.
QUESTION 9 Two vertical forces act on a skydiver with a mass of 85 kg as shown. Alir resistance A = y Weight When the magnitude of the air resistance is 62 N the magnitude of the acceleration of the skydiver is (A) 073ms 2 (B) 2.65ms (C) 9.07ms™> (D) 12.44ms™>
QUESTION 17 (7 marks) An object with a mass of 2 kg is released from rest at the top of a 1 metre long frictionless plane inclined at 30° to the horizontal. A force of P newtons acting parallel to the plane opposes the motion of the object as it travels down the plane. When the object is x metres from the top of the plane its velocity is v m s 4 Va4 -—x? ’ Given ‘P| = determine x when v = 2.
QUESTION 7 Two forces act concurrently on a 2 kg object placed at the origin. y Not to scale The magnitude of the acceleration of the object is (A) 2m 572 (B) 23 ms™ (C) 4ms™> (D) 43 ms™
QUESTION 6 A 4 kg object moves in a straight line over time z‘(s) where 0 < ¢ < 5 with velocity v = 9 + 8¢ — 1> (m g7 ) Determine the momentum of the object when ¢ = 3. (A) 24kgms! (B) 27kgm s (C) 96kgm s (D) 100 kg m s
QUESTION 16 (6 marks) An object with a mass of 12 kg lies on a frictionless inclined plane. A rope is attached to the object at an angle of 25° above the plane as shown. Not to scale The force of the rope T N prevents the object from moving. When the rope is detached the object moves down the plane with an acceleration of 5.6 m §72 Determine the magnitude of T.
QUESTION 4 An object lies on a horizontal plane as shown in the diagram below. When a force of 350 N is applied at an angle of 20° the object remains stationary. @ Not drawn to scale The frictional force acting on the object correct to the nearest unit is (A) 119N (B) 120N (C) 328N (D) 329N
QUESTION 10 The velocity v (m s~ 1) of a particle at time ¢t (s) is given by v = sin 1(¢) (0 <t < 15). The acceleration of the particle when t = 0.2 s is (A) 0.20ms™2 (B) 1.02ms™? (C) 1.04ms™2 (D) 1.37ms™2
QUESTION 18 (7 marks) An object of mass 5 kg moves in a straight line while being acted on by a net force F (N) in terms of its position from a reference point x (5 m < x < 10 m) such that 60 + 5x T 12x— 7%+ 3 Given the object was at rest when x = 5 m determine the position of the object from the reference point when its speed is 0.5 m s™.
QUESTION 17 (7 marks) An object of mass 2 kg is moving with a constant velocity (m sg!) of v=3i +k. At an instant two forces (N) F = Stj- 3k and F = -tj+ k act simultaneously on the object for t seconds where 0<¢ <2. Determine the magnitude of the momentum of the object when ¢t=1.
QUESTION 1 The acceleration (m s) of an object moving with simple harmonic motion is modelled by a = —2.95x where x is its displacement (m) from the origin. Determine the period of the motion in seconds. (A) 1.72 (B) 2.13 (C) 2.95 (D) 3.66
QUESTION 6 Two coplanar forces of magnitudes 12 N and 10 N act on an object in the directions shown. Not to scale y 22° 10N 12N Determine the magnitude of the resultant force acting on the object. (A) 12.41 N (B) 15.55N (C) 15.69N (D) 18.27N
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