Question

1. 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: Recall average - velocity formula

The formula for average velocity $v_{avg}=\frac{\Delta x}{\Delta t}$. But we can also use the formula for average velocity when the motion has constant - acceleration or when we know the initial and final velocities. The formula $v_{avg}=\frac{v_i + v_f}{2}$ can be used. The canoeist paddles upstream at $v_i = 2.0\ m/s$ for $t_1=4.0\ s$, then floats downstream at $v_f = 4.0\ m/s$ for $t_2 = 4.0\ s$. The total time $\Delta t=t_1 + t_2=8.0\ s$.

Step2: Calculate average velocity

Using $v_{avg}=\frac{v_i + v_f}{2}$, where $v_i = 2.0\ m/s$ and $v_f = 4.0\ m/s$. So $v_{avg}=\frac{2.0+4.0}{2}=3.0\ m/s$.

Step3: Recall average - acceleration formula

The formula for average acceleration is $a_{avg}=\frac{\Delta v}{\Delta t}=\frac{v_f - v_i}{\Delta t}$.

Step4: Calculate average acceleration

Here, $v_i = 2.0\ m/s$, $v_f = 4.0\ m/s$ and $\Delta t=8.0\ s$. Then $a_{avg}=\frac{4.0 - 2.0}{8.0}=\frac{2.0}{8.0}=0.25\ m/s^2$.

Answer:

a. The average velocity is $3.0\ m/s$.
b. The average acceleration is $0.25\ m/s^2$.