Question

2)define: acceleration: the rate of change of velocity this question has two parts. the graph below shows the velocity of an object over time. a = \\(\frac{\delta v}{\delta t}\\) or \\(\frac{v_f - v_i}{t_f - t_i}\\) at what time does the graph show the greatest change in acceleration or deceleration? what is the acceleration or deceleration? a) 0 to 3 seconds b) 3 to 8 seconds c) 8 to 10 seconds acceleration or deceleration of ____ m/s²

Explanation:

Step1: Recall acceleration formula

Acceleration $A=\frac{\Delta V}{\Delta T}=\frac{V_f - V_i}{T_f - T_i}$, where $\Delta V$ is change in velocity and $\Delta T$ is change in time.

Step2: Analyze each time - interval

• For 0 to 3 seconds: $V_i = 0$, $V_f=30$, $\Delta T = 3$, $A_1=\frac{30 - 0}{3-0}=10\ m/s^2$.
• For 3 to 8 seconds: $V_i = 30$, $V_f = 30$, $\Delta T=8 - 3 = 5$, $A_2=\frac{30 - 30}{8 - 3}=0\ m/s^2$.
• For 8 to 10 seconds: $V_i = 30$, $V_f = 0$, $\Delta T=10 - 8 = 2$, $A_3=\frac{0 - 30}{10 - 8}=- 15\ m/s^2$.

Step3: Compare accelerations

The magnitudes of the accelerations are $|A_1| = 10\ m/s^2$, $|A_2| = 0\ m/s^2$, $|A_3| = 15\ m/s^2$. The greatest change in acceleration (or deceleration) occurs in the 8 - 10 seconds interval.

Answer:

C. 8 to 10 seconds, acceleration or deceleration of $-15\ m/s^2$