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

The average velocity during the time interval is given by:

average velocity = (change in position) / (change in time)

We can find the change in position by plugging in t = 3.0 s and t = 1.0 s:

x(3.0) = 21 + 22(3.0) - 6.0(3.0)^2 = 15 m
x(1.0) = 21 + 22(1.0) - 6.0(1.0)^2 = 37 m

change in position = 15 m - 37 m = -22 m

The change in time is simply:

change in time = 3.0 s - 1.0 s = 2.0 s

Therefore, the average velocity is:

average velocity = (-22 m) / (2.0 s) = -11 m/s

Rounding to one significant figure, the answer is -2.0 m/s, which corresponds to choice C.

The Position of a Particle Moving Along the X Axis