Question

8 the velocity of a bus is represented in the graph below. velocity of bus over time which of the following best describes how the bus moves over time? a the bus stays in one place for 20 s and then travels at a constant speed. b the bus travels at a constant speed for 20 s and then accelerates at a constant rate. c the bus accelerates at a constant rate for 20 s and then travels at a constant speed. d the bus accelerates at a constant rate for 20 s and then accelerates at an increasing rate.

Explanation:

Step1: Analyze the first part of the graph

For the first \(20\) seconds, the velocity - time graph is a horizontal line. In a velocity - time graph, a horizontal line means that the velocity \(v\) is constant (\(\Delta v=0\)). Using the formula for acceleration \(a = \frac{\Delta v}{\Delta t}\), since \(\Delta v = 0\), the acceleration \(a = 0\) for \(t\in[0,20]\) s. So, the bus is moving at a constant speed for the first \(20\) seconds.

Step2: Analyze the second part of the graph

For \(t > 20\) s, the velocity - time graph is a straight - line with a positive slope. The formula for the slope of a velocity - time graph is \(m=\frac{\Delta v}{\Delta t}\), and this slope represents the acceleration. Since the slope \(m>0\) and is constant (because it's a straight line), the acceleration \(a=\frac{\Delta v}{\Delta t}\) is constant for \(t > 20\) s.

Answer:

B. The bus travels at a constant speed for \(20\) s and then accelerates at a constant rate.