Question

1. velocity - time graph sketch a b - time graph for a car that goes east at 25 m/s for 100 s, then west at 25 m/s for another 100 s. 14. average velocity and average acceleration a canoeist paddles upstream at a velocity of 2.0 m/s for 4.0 s and then floats downstream at 4.0 m/s for 4.0 s. a. what is the average velocity of the canoe during the 8.0 - s time interval? b. what is the average acceleration of the canoe during the 8.0 - s time interval?

Explanation:

Step1: Calculate the total displacement for the canoe's motion

The canoe moves upstream at a velocity \(v_1 = 2.0\ m/s\) for \(t_1=4.0\ s\). The displacement \(d_1=v_1t_1 = 2.0\times4.0=8.0\ m\) (up - stream). Then it moves downstream at \(v_2 = 4.0\ m/s\) for \(t_2 = 4.0\ s\). The displacement \(d_2=v_2t_2=4.0\times4.0 = 16.0\ m\) (down - stream). The net displacement \(d=d_2 - d_1=16.0 - 8.0=8.0\ m\) (down - stream).

Step2: Calculate the average velocity

The total time interval \(t=t_1 + t_2=4.0+4.0 = 8.0\ s\). The average velocity \(v_{avg}=\frac{d}{t}\). Substituting \(d = 8.0\ m\) and \(t = 8.0\ s\) into the formula, we get \(v_{avg}=\frac{8.0}{8.0}=1.0\ m/s\) (down - stream).

Answer:

\(1.0\ m/s\) (down - stream)