Question

velocity vs time
what is the acceleration of the car at segment c?
30 m/s²
-30 m/s²
40 m/s²
-40 m/s²

Explanation:

Step1: Recall the formula for acceleration

Acceleration \(a=\frac{\Delta v}{\Delta t}\).

Step2: Identify \(\Delta v\) and \(\Delta t\) for segment C

From the graph, at the start of segment C (let's say \(t = 5s\)), \(v_{initial}=40m/s\) and at the end of segment C (\(t = 7s\)), \(v_{final} = 10m/s\). So \(\Delta v=v_{final}-v_{initial}=10 - 40=- 30m/s\) and \(\Delta t=7 - 5 = 2s\).

Step3: Calculate acceleration

\(a=\frac{\Delta v}{\Delta t}=\frac{-30}{2}=-15m/s^{2}\) (Wait, no. Wait, maybe mis - read the graph. Wait, another approach: slope of velocity - time graph.
The formula for acceleration from a velocity - time graph is \(a=\text{slope}=\frac{y_2 - y_1}{x_2 - x_1}\).
Assume at \(t = 5s\), \(v = 40m/s\) and at \(t=6s\), \(v = 10m/s\) (if we consider a steeper slope for calculation as per options). Then \(\Delta v=10 - 40=-30m/s\) and \(\Delta t = 6 - 5=1s\).
\(a=\frac{\Delta v}{\Delta t}=\frac{10 - 40}{6 - 5}=- 30m/s^{2}\)

Answer:

\(-30m/s^{2}\)