Question

Which of the following answers to the question below is correct (multiple answers can be chosen)?

Question: Let s(t) be the position of a moving particle at time t. Choose ALL that represent the average speed of the particle over the time interval [0,4]?

1. s(4)/4
2. s(4)-s(0)/4
3. The slope of the secant line from (0, s(0)) to (4, s(4))
4. The slope of the tangent line at (0, s(0))​

Answer 1

the correct answers are, 2 and 3

Answer 2

The average speed of a particle over a time interval is defined as the total distance traveled divided by the time elapsed. In this case, the average speed of the particle over the time interval [0,4] is represented by options 2 and 3. Option 2 represents the change in position over the time interval [0,4] divided by the time elapsed. Option 3 represents the slope of the secant line connecting the points (0,s(0)) and (4,s(4)), which is equivalent to the average rate of change of position over the time interval [0,4].