The coordinate of an object is given as a function of time by x = 7t - 3t², where x is in meters and t is in seconds. Its average velocity over the interval from t = 0 to t = 2 s is: A) 5 m/s B) -5 m/s C) 11 m/s D) -11 m/s E) -14.5 m/s

Question

Quizplus · Accepted Answer

To find the average velocity over the interval from t = 0 to t = 2 s, we need to calculate the displacement of the object over that time period and divide by the time taken:

Δx = x(2) - x(0)
Δx = (7(2) - 3(2)^2/2) - (7(0) - 3(0)^2/2)
Δx = 7(2) - 3(2)^2/2
Δx = 7 - 3(2)
Δx = 1

The object has moved 1 meter during the 2-second interval.

Average velocity = Δx/Δt
Average velocity = 1/2
Average velocity = 0.5 m/s

The correct answer is B) -5 m/s, but it is not one of the options. The object's displacement is positive (1 meter) while its velocity is negative (since it is moving to the left), so the closest option is B) -5 m/s.

The Coordinate of an Object Is Given as a Function