The velocity of a particle in rectilinear motion changes to the right to 12 ft/s

Question

The velocity of a particle in rectilinear motion changes to the right to 12 ft/sec to the left; the acceleration is a constant the left. Determine the total time interval required for this velocity. Find the displacement and the distance traveled interval. Ans. : 47.2 ft to right; 65.2 ft. The pin, Q, is fixed on the rim of the 3-in disk that can rotate about its center, O. The pin is forced to move in the slot of the yoke P that moves upward at a constant speed of 6 in/sec. Find the velocity and acceleration of Q at a time when theta = 53 degree. Sketch these vectors to show their relation to the line OQ. (Hint:use the method of Example 1.8-3 atthis time.) Ans.: v = 8i-6j, a =-55middot5i (in, sec); x+ to right, y+ down. An electron moves in an electric field such that its dis given by x = 0.08 sin 5t, y = 0.06 cos 5t, z=0, where distances and time in seconds. Find the maximum and minimum magnitudes. Ans.: amax = 2 m/sec2; amin = 1.5 m/sec2. A particle moves on the path x = 3 sin 5t, y 3 3/2 cos 5t, when t is in seconds. Find the acceleration and show that it magnitude. How is the path of this problem related Example 1.8-1? Same motion, referred to new axes. The velocity of a particle is given by The velocity of a particle in rectilinear motion changes to the right to 12 ft/sec to the left; the acceleration is a constant the left. Determine the total time interval required for this velocity. Find the displacement and the distance traveled interval. Ans. : 47.2 ft to right; 65.2 ft. The pin, Q, is fixed on the rim of the 3-in disk that can rotate about its center, O. The pin is forced to move in the slot of the yoke P that moves upward at a constant speed of 6 in/sec. Find the velocity and acceleration of Q at a time when theta = 53 degree. Sketch these vectors to show their relation to the line OQ. (Hint:use the method of Example 1.8-3 atthis time.) Ans.: v = 8i-6j, a =-55middot5i (in, sec); x+ to right, y+ down. An electron moves in an electric field such that its dis given by x = 0.08 sin 5t, y = 0.06 cos 5t, z=0, where distances and time in seconds. Find the maximum and minimum magnitudes. Ans.: amax = 2 m/sec2; amin = 1.5 m/sec2. A particle moves on the path x = 3 sin 5t, y 3 3/2 cos 5t, when t is in seconds. Find the acceleration and show that it magnitude. How is the path of this problem related Example 1.8-1 ? Same motion, referred to new axes. The velocity of a particle is given by

Explanation / Answer

for yoke problem vertical velocity =6 angle is 53 hence in direction of tangent velocity=Vt = 6/cos53 =10 horizontal velocity =Vt*sin 53 =(6/cos53)*sin 53 =6tan53 =8 hence v =8i-6j ... effective radius around which it rotates =3cos53 acc v^2/r =10^2/3 =100/3cos53 =55.5 in/s

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