You are the mechatronics engineer of a manufacturing plant. You decide to perform an analysis on a robot arm of the assembly line with the objective of optimizing its performance. After taking several readings of the speed of the arm’s end effector, you approximate its velocity to the function given below. v(t) = -t4 + 5t3 - 7t2 + 3t + 0.22 0 =< t =< 3 where the velocity is in ms-1 d) Knowing that the distance travelled by an object is the area under its velocity-time graph, determine the distance travelled by the end effector on the interval 0 =< t =< 1 by using the mid-ordinate rule. Simpson’s rule correct to 3 decimal places using four intervals. e) Calculate the same distance as in (d) above by using the appropriate definite integral. f) Compare the distances you calculated in (d) and (e) above and comment on the accuracy of the two methods you used in (d)
You are the mechatronics engineer of a manufacturing plant. You decide to perform an analysis on a robot arm of the assembly line with the objective of optimizing its performance. After taking several readings of the speed of the arm’s end effector, you approximate its velocity to the function given below.
v(t) = -t4 + 5t3 - 7t2 + 3t + 0.22 0 =< t =< 3
where the velocity is in ms-1
d) Knowing that the distance travelled by an object is the area under its velocity-time graph, determine the distance travelled by the end effector on the interval 0 =< t =< 1 by using
-
- the mid-ordinate rule.
- Simpson’s rule
correct to 3 decimal places using four intervals.
e) Calculate the same distance as in (d) above by using the appropriate definite integral.
f) Compare the distances you calculated in (d) and (e) above and comment on the accuracy of the two methods you used in (d)
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