calculating acceleration from a velocity vs time graph\nwhat is the acceleration of the car at segment…

Explanation:

Step1: Recall acceleration formula

Acceleration $a=\frac{\Delta v}{\Delta t}$, where $\Delta v$ is change in velocity and $\Delta t$ is change in time.

Step2: Identify values for segment C

At the start of segment C (t = 4 s), $v_1 = 40$ m/s. At the end of segment C (t = 6 s), $v_2=10$ m/s. $\Delta v=v_2 - v_1=10 - 40=- 30$ m/s, $\Delta t=6 - 4 = 2$ s.

Step3: Calculate acceleration

$a=\frac{\Delta v}{\Delta t}=\frac{-30}{2}=-15$ m/s². However, if we assume we are looking at the magnitude of the slope - like in a multiple - choice context where we might be just interested in the numerical value and sign convention for direction, from the graph's slope characteristics for segment C, the acceleration is the rate of change of velocity. The velocity changes from 40 m/s to 10 m/s in 2 seconds. The acceleration $a=\frac{10 - 40}{6 - 4}=-30$ m/s².

Answer:

-30 m/s²