Question

using velocity vs time graphs to find acceleration
velocity vs time
the acceleration of segment d is m/s².
rank segments a, b, and c from least acceleration to greatest acceleration.
least:
greatest:

Explanation:

Step1: Calculate acceleration of segment D

Acceleration \(a=\frac{\Delta v}{\Delta t}\). For segment D, \(v_{initial} = 20\ m/s\), \(v_{final}=0\ m/s\), \(t_{initial}=4\ s\), \(t_{final} = 5\ s\).
\(a=\frac{0 - 20}{5 - 4}=\frac{- 20}{1}=- 20\ m/s^{2}\)

Step2: Analyze slopes for segments A, B, C

The acceleration is the slope of the velocity - time graph.
For segment A: \(v_{initial}=0\ m/s\), \(v_{final}=15\ m/s\), \(t_{initial}=0\ s\), \(t_{final}=1\ s\), \(a_{A}=\frac{15 - 0}{1-0}=15\ m/s^{2}\)
For segment B: \(v_{initial}=15\ m/s\), \(v_{final}=20\ m/s\), \(t_{initial}=1\ s\), \(t_{final}=2\ s\), \(a_{B}=\frac{20 - 15}{2 - 1}=5\ m/s^{2}\)
For segment C: Since it is a horizontal line (constant velocity), \(a_{C}=0\ m/s^{2}\)

Answer:

The acceleration of segment D is \(-20\ m/s^{2}\).
Rank: Least: C, then B, then A (Greatest).