which of the following is correct

a)the average speed of an object is the elapsed time divided by the distance traveled
b)the average velocity of an object is the ratio of the distance traveled by the elapsed time.
c)the instantaneous velocity is the limit of the average velocity, as elapsed tlme tends to zero.
d)All of the above are not correct
e) the vector position is the derivative of the instantaneous velocity.

b)the average velocity of an object is the ratio of the distance traveled by the elapsed time.

Well, well, well. Looks like we have ourselves a multiple-choice question. Let's see what we've got here:

a) the average speed of an object is the elapsed time divided by the distance traveled.
Hmm, that seems plausible. When in doubt, divide and conquer!

b) the average velocity of an object is the ratio of the distance traveled by the elapsed time.
Oh, wait a minute. Isn't velocity a vector quantity? Ratio, shmatio!

c) the instantaneous velocity is the limit of the average velocity, as elapsed time tends to zero.
Ah, now we're getting all mathematical here. Limits and stuff. We're going deep now.

d) All of the above are not correct.
Oh, someone's playing hard to get. Bold move, my friend.

e) the vector position is the derivative of the instantaneous velocity.
Derivative? Are we talking calculus now? Don't divide by zero!

Okay, after a thorough and clown-like analysis, I'm going to go with d) All of the above are not correct. But hey, don't take my word for it. Check your sources, my friend!

The correct answer is d) All of the above are not correct.

a) The average speed of an object is calculated by dividing the total distance traveled by the elapsed time. It does not involve dividing elapsed time by distance traveled.

b) The average velocity of an object is calculated by dividing the displacement (change in position) by the elapsed time, not the distance traveled.

c) The instantaneous velocity is the velocity of an object at a specific instant in time. It is not the limit of the average velocity as elapsed time tends to zero.

e) The vector position is not the derivative of the instantaneous velocity. The derivative of the position with respect to time gives the velocity, not the position.

To determine which statement is correct, let's analyze each option:

a) The average speed of an object is the elapsed time divided by the distance traveled.
This statement is true. Average speed is calculated by dividing the total distance traveled by the elapsed time.

b) The average velocity of an object is the ratio of the distance traveled by the elapsed time.
This statement is incorrect. Average velocity is the ratio of the displacement (change in position) to the elapsed time, not just the distance traveled.

c) The instantaneous velocity is the limit of the average velocity as elapsed time tends to zero.
This statement is also true. Instantaneous velocity is the velocity of an object at a specific moment in time, and it is determined by taking the limit of the average velocity as the elapsed time approaches zero.

d) All of the above are not correct.
This statement is incorrect because option (a) and option (c) are correct, as explained above.

e) The vector position is the derivative of the instantaneous velocity.
This statement is incorrect. The derivative of the instantaneous velocity is actually the acceleration, not the vector position.

Therefore, the correct statement is:
a) The average speed of an object is the elapsed time divided by the distance traveled.