Question

An object moves along a straight line so that at any time t, for 0 < t < 8, its position is given by x(t) = 5(4t - t^2)...

Option 1: (4, 0)
Option 2: (2, 8)
Option 3: (-2, -24)
Option 4: (6, 20)

Answer 1

Upon calculating the position at different times using the function x(t) = 5(4t - t^2), Option 2 with the coordinates (2, 20) is the correct position-time pair for the object's movement.

Step-by-step explanation:

The student is asking about an object moving in a straight line, which involves finding the position at a specific time using the position function given by x(t) = 5(4t - t^2). To determine which option of position at a given time is correct, we can plug the time value from each option into the function and calculate the position.

1. For Option 1: x(4) = 5(4(4) - 4^2) = 5(16 - 16) = 5(0) = 0.
2. For Option 2: x(2) = 5(4(2) - 2^2) = 5(8 - 4) = 5(4) = 20.
3. For Option 3: Since the time 't' must be between 0 and 8, this option is not possible as the time cannot be negative.
4. For Option 4: x(6) = 5(4(6) - 6^2) = 5(24 - 36) = 5(-12) = -60.

Therefore, Option 2: (2, 20) is the correct position-time pair for the object's movement according to the provided function.