A mouse runs along a baseboard in your house. The mouse's position as a function of time is given by x (t) = pt2+qt, with p = 0.36 m/s2 and q = - 1.20 m/s.

Determine the mouse's average speed between t=1.0s and t=4.0s

0.60 m/s

Explanation:

The average velocity from t = a to t = b is:

v_avg = (x (b) - x (a)) / (b - a)

Given that x (t) = 0.36t² - 1.20t, and the time is from 1.0 to 4.0:

v_avg = (x (4.0) - x (1.0)) / (4.0 - 1.0)

v_avg = [ (0.36 (4.0) ² - 1.20 (4.0)) - (0.36 (1.0) ² - 1.20 (1.0)) ] / 3.0

v_avg = [ (5.76 - 4.8) - (0.36 - 1.20) ] / 3.0

v_avg = [0.96 - (-0.84) ] / 3.0

v_avg = 0.60

The average speed is 0.60 m/s.