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.

Solution Summary

Tis posting contains the solution to the given problems.

... Tangential acceleration is due to the change in magnitude of velocity of the particle whereas centripetal acceleration is due to the change in direction of ...

... 4: So particle 3 and 4 has constant acceleration. ... the velocity, then the magnitude of the velocity is the ...Particle 1: Particle 2: Particle 3: Particle 4: For ...

... speed, rotation, particles, power, degrees, axis. 1. At t=0, a fly wheel has an angular velocity of 4.7 rad/s (radians per second), an angular acceleration of ...

... both velocities have the same magnitude (the length of the ... have change in the direction of the velocity, we must ... The acceleration a of a body is parallel and ...

A rocket is modelled by a particle that moves along a ... launch pad and attained an upward velocity of 70ms ... the rocket has a constant upward acceleration of −10 ...

... The average velocity of a particle moving in the x ... tf − ti and the average speed of a particle is given ... (3) total time Finally, the average acceleration of a ...