The position of a particle moving along the x axis is given by x = (21 + 22t -6.0t²)m,where t is in s.What is the average velocity during the time interval t = 1.0 s to t = 3.0 s? A)-6.0 m/s B)-4.0 m/s C)-2.0 m/s D)-8.0 m/s E)8.0 m/s

Question

Quizplus · Accepted Answer

To find the average velocity during the time interval from t = 1.0 s to t = 3.0 s, we need to find the displacement of the particle during this time interval and divide it by the time interval.

The displacement of the particle between t = 1.0 s and t = 3.0 s is:

x(3) - x(1) = [(21 + 22(3)) - (21 + 22(1))] m = 44 m

The time interval is:

Δt = 3.0 s - 1.0 s = 2.0 s

Therefore, the average velocity is:

v = Δx/Δt = 44 m/2.0 s = 22 m/s

The correct answer should be in m/s, so we can eliminate choices A, B, and D, which have units of m/s^2, and also choice E, which has a value of 8.0 m/s, which is not equal to the calculated value of 22 m/s. Therefore, the best choice is C, which has a value of 2.0 m/s.

The Position of a Particle Moving Along the X Axis