Question

The end of the industrial robotic arm extends along the path (r = 2 + 2 cos (5t)) m. At the instant ( 0 = 0.8t ) radians. When the arm is located at (t = 0.85) second Determine the velocity and acceleration of the object A at this instant.​

Answer 1

Answer:

  v = 8.95 rad / s,    a = 22.3 rad / s²

Explanation:

This is an exercise in kinematics, where we must use the definitions of velocity and acceleration

          v = dr / dt

       

we perform the derivative

          v = 0+ 2 (-sin 5t) 5

          v = -10 sin 5t

we calculate for t = 0.85 t,

remember angles are in radians

           v = -10 sin (5 0.85)

           v = 8.95 rad / s

acceleration is defined by

           a = dv / dt

             

we perform the derivatives

          a = -10 (cos 5t) 5

          a = - 50 cos 5t

we calculate for t = 0.85 s

          a = -50 are (5 0.85)

          a = 22.3 rad / s²