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

v = 8.95 rad / s, a = 22.3 rad / s²

Step-by-step 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