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Acceleration and Velocity of a Particle

1. A particle oscillates between the points x = 40 mm and x = 160 mm with an acceleration a = k( 100 - x), where a and x are expressed in mm/ s^2 and mm, respectively, and k is a constant. The velocity of the particle is 18 mm/ s when x = 100 mm and is zero at both x = 40 mm and x = 160 mm. Determine (a) the value of k,( b) the velocity when x = 120 mm.

2. The motion of a particle is defined by the relation x = 1.5t^4 - 30t2 + 5t + 10, where x and t are expressed in meters and seconds, respectively. Determine the position, the velocity, and the acceleration of the particle when t = 4 s.

3. The acceleration of a particle is defined by the relation a = kt^2. (a) Knowing that v =-32 ft/ s when t = 0 and that v =-32 ft/ s when t = 4 s, determine the constant k. ( b) Write the equations of motion, knowing also that x = 0 when t = 4 s.

4. A truck travels 220 m in 10 s while being decelerated at a constant rate of 0.6 m/ s^2. Determine (a) its initial velocity, ( b) its final velocity, ( c) the distance traveled during the first 1.5 s.

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