Question

1 acceleration (continued)

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: Calcular los desplazamientos

Definimos que el movimiento upstream es negativo. El desplazamiento $d_1$ upstream es $d_1 = v_1t_1=(- 2.0\ m/s)\times4.0\ s=-8.0\ m$. El desplazamiento $d_2$ downstream es $d_2 = v_2t_2=(4.0\ m/s)\times4.0\ s = 16.0\ m$.

Step2: Calcular el desplazamiento total

El desplazamiento total $d=d_1 + d_2=-8.0\ m+16.0\ m = 8.0\ m$.

Step3: Calcular la velocidad media

La velocidad media $v_{avg}=\frac{d}{t_{total}}$, donde $t_{total}=8.0\ s$. Entonces $v_{avg}=\frac{8.0\ m}{8.0\ s}=1.0\ m/s$.

Step4: Calcular la velocidad inicial y final

La velocidad inicial $v_i=-2.0\ m/s$ y la velocidad final $v_f = 4.0\ m/s$.

Step5: Calcular la aceleración media

La aceleración media $a_{avg}=\frac{v_f - v_i}{t_{total}}=\frac{4.0\ m/s-(-2.0\ m/s)}{8.0\ s}=\frac{6.0\ m/s}{8.0\ s}=0.75\ m/s^{2}$.

Answer:

a. $1.0\ m/s$
b. $0.75\ m/s^{2}$