Question

1. which option best describes the average acceleration from 40 to 70 s? a. it is negative and smaller in magnitude than the initial acceleration. b. it is negative and larger in magnitude than the initial acceleration. c. it is positive and smaller in magnitude than the initial acceleration. d. it is positive and larger in magnitude than the initial acceleration.

Explanation:

Step1: Recall acceleration formula

Acceleration $a=\frac{\Delta v}{\Delta t}$, where $\Delta v = v_f - v_i$ and $\Delta t=t_f - t_i$.

Step2: Determine $v_i$, $v_f$, $t_i$ and $t_f$ from graph

At $t_i = 40\ s$, $v_i\approx240\ m/s$. At $t_f = 70\ s$, $v_f\approx240\ m/s$. So $\Delta t=70 - 40=30\ s$ and $\Delta v=240 - 240 = 0\ m/s$.

Step3: Calculate average - acceleration

$a=\frac{\Delta v}{\Delta t}=\frac{0}{30}=0\ m/s^2$. Initially (from $t = 0$ to $t = 10\ s$), the velocity is increasing, so the initial acceleration is positive. Since the average acceleration from $40$ to $70\ s$ is $0$, it is positive (compared to negative values) and smaller in magnitude than the non - zero initial acceleration.

Answer:

c. It is positive and smaller in magnitude than the initial acceleration.