Question

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

Answer 1

Answer:

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.