Question

the velocity versus time graph of particle a is tangent to the velocity versus time graph for particle b at point o. what is the acceleration of the particle a at point o?
a. -0.85 meters/second²
b. 1.16 meters/second²
c. -1.16 meters/second²
d. -0.9 meters/second²

Explanation:

Step1: Recall acceleration definition

Acceleration is the slope of the velocity-time graph, calculated as $\text{slope} = \frac{\Delta v}{\Delta t} = \frac{v_2 - v_1}{t_2 - t_1}$. For particle A at point O, we use the tangent line (particle B's graph) to find this slope.

Step2: Select points on line B

Choose two clear points on line B: $(t_1, v_1) = (0, 14)$ and $(t_2, v_2) = (12, 0)$.

Step3: Calculate the slope

$$ \text{Acceleration} = \frac{0 - 14}{12 - 0} = \frac{-14}{12} \approx -1.16 $$

Answer:

C. -1.16 meters/second²