Question

1. position-time graph

the graph above represents a car driving down a straight highway. what is the acceleration from 0-4 seconds?
options:
○ 0 m/s²
○ 5 m/s²
○ 10 m/s²
○ 20 m/s²
clear all

Explanation:

Step1: Analyze the position - time graph

A position - time graph with a straight line (constant slope) represents an object moving with a constant velocity. The slope of a position - time graph is given by the formula \(v=\frac{\Delta x}{\Delta t}\), where \(\Delta x\) is the change in position and \(\Delta t\) is the change in time. For a straight - line position - time graph, the velocity \(v\) is constant.

Step2: Recall the relationship between velocity and acceleration

Acceleration \(a\) is defined as the rate of change of velocity, i.e., \(a = \frac{\Delta v}{\Delta t}\). If the velocity \(v\) is constant ( \(\Delta v=0\) ), then the acceleration \(a=\frac{0}{\Delta t} = 0\) for any time interval \(\Delta t\) (as long as \(\Delta t
eq0\)). Since the position - time graph is a straight line (constant velocity) from \(t = 0\) to \(t=4\) seconds, the velocity does not change, so the acceleration is \(0\space m/s^{2}\).

Answer:

\(0\space m/s^{2}\)