Question

The position of an object moving along an x axis is given by x = 3.09 t - 4.08 t2 + 1.09 t3, where x is in meters and t in seconds. Find the position of the object at the following values of t: (a) 1 s, (b) 2 s, (c) 3 s, and (d) 4 s. (e) What is the object's displacement between t = 0 and t = 4 s? (f) What is its average velocity from t = 2 s to t = 4 s?

Answer 1

To find an object's location at different times and calculate displacement and average velocity, you should use the given position equation, injecting the required time values into it. The difference between the object's locations at the two times is displacement, and average velocity is total displacement divided by total time.

Step-by-step explanation:

The position of an object moving along an x-axis is given by x = 3.09t - 4.08t² + 1.09t³. To find the position of the object at different times, we simply plug the time values into the equation. For example:

1. For t = 1s, x = 3.09(1) - 4.08(1)² + 1.09(1)³.
2. For t = 2s, x = 3.09(2) - 4.08(2)² + 1.09(2)³.
3. For t = 3s, x = 3.09(3) - 4.08(3)² + 1.09(3)³.
4. For t = 4s, x = 3.09(4) - 4.08(4)² + 1.09(4)³.

Next, to calculate the displacement between t = 0s and t = 4s, we calculate the difference in the object's position at these two times. Let's say x(0) = initial position and x(4) = final position, then displacement = x(4) - x(0).

Finally, to find its average velocity from t = 2s to t = 4s, remember that average velocity is Total displacement / Total time = [x(4) - x(2)] / (4-2).

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