Question

question 8 (1 point)
the graph below shows the relationship between the speed and elapsed time for an object falling freely from rest near the surface of a planet.
what is the velocity of the object at 3 seconds?
graph: speed vs. time, x - axis (time in s): 0, 1.0, 2.0, 3.0, 4.0; y - axis (speed in m/s): 0, 2.0, 4.0, 6.0, 8.0, 10.0; a line from (0,0) to (4,10) - like, with grid
options:
○ a 6m/s
○ b 4m/s
○ c 8m/s
○ d 5m/s

Explanation:

Step1: Analyze the graph

The graph is a speed - time graph for an object in free fall. We can see that the graph is a straight line, so the speed and time have a linear relationship. Let's find the slope (acceleration) first. From the graph, when \(t = 2\) s, \(v=6\) m/s (or we can use other points). The slope \(m=\frac{\Delta v}{\Delta t}\). Let's take two points, say \((0,0)\) and \((2,6)\). Then \(m = \frac{6 - 0}{2 - 0}=3\) m/s².

Step2: Use the linear equation

The equation of a line is \(v=v_0+at\). Since the object starts from rest, \(v_0 = 0\) m/s. So \(v=at\). We found \(a = 3\) m/s²? Wait, no, wait. Wait, when \(t = 3\) s, let's look at the graph. Wait, the graph: on the x - axis, time is in seconds, y - axis speed in m/s. At \(t = 3\) s, looking at the grid, the y - value (speed) at \(x = 3\) (time = 3 s) is 6 m/s? Wait, no, wait the options: a is 6 m/s, b is 4, c is 8, d is 5. Wait, let's check the graph again. The graph has time from 0 to 4 s, speed from 0 to 10 m/s. At \(t = 2\) s, speed is 6? Wait, no, maybe I misread. Wait, the grid: each square on x - axis is 1 s, on y - axis, let's see, from 0 to 2 is one square? Wait, no, the y - axis: 0, 2.0, 4.0, 6.0, 8.0, 10.0. So each major grid line is 2 m/s? Wait, no, the labels: 2.0, 4.0, 6.0, 8.0, 10.0. So at \(t = 1\) s, speed is 2 m/s? Wait, no, the line passes through (1, 2), (2, 4), (3, 6), (4, 8)? Wait, no, the original graph: the user's graph: "Speed vs. Time" with y - axis speed (m/s) labeled 0, 2.0, 4.0, 6.0, 8.0, 10.0. x - axis time (s) 0, 1.0, 2.0, 3.0, 4.0. The line goes from (0,0) to (4,10)? No, wait the options. Wait, the options are 6,4,8,5. Wait, maybe the slope is 2? Wait, at \(t = 3\) s, if we look at the graph, when time is 3 seconds, the speed is 6 m/s? Wait, no, maybe the graph is such that at \(t = 3\) s, the speed is 6 m/s. Let's check the options. Option a is 6 m/s.

Answer:

a. 6m/s