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.​

  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

the warning light flashes for a second or two when the engine starts. if it stays on, there's must be something wrong with the coolant. you should never dare to continue driving when the light is on. pull over as soon as possible and shut the engine off.

hope this is what you're talking about