Question
Which is the independent variable? __ Which is the dependent variable? __ Where was the object at 4 seconds? __ Find the slope of the graph (must show work) What does the slope you just found stand for? __
Answer
3.7
(184 Votes)
Benjamin
Master · Tutor for 5 years
Answer
Step 1: Identify the Independent and Dependent VariablesIn a position-time graph, the independent variable is typically the time, and the dependent variable is the position. This is because the position of an object depends on the time at which it is measured.Answer:- The independent variable is time (in seconds).- The dependent variable is position (in meters).Step 2: Determine the Position at 4 SecondsTo find the position of the object at 4 seconds, we need to use the information given about the graph. Since the graph is a straight line, we can use the two points provided to find the equation of the line and then use that equation to find the position at 4 seconds.Step 3: Find the Slope of the GraphThe slope of a line on a graph is calculated by the change in the vertical axis (position) divided by the change in the horizontal axis (time). Using the points (0,2) and (2,8):Slope (m) = (Change in position) / (Change in time) = (Position at second point - Position at first point) / (Time at second point - Time at first point) = (8 - 2) / (2 - 0) = 6 / 2 = 3Answer: The slope of the graph is 3.Step 4: Interpret the SlopeThe slope of a position-time graph represents the velocity of the object. This is because velocity is defined as the rate of change of position with respect to time.Answer: The slope of 3 meters per second stands for the velocity of the object.Step 5: Use the Slope to Find the Position at 4 SecondsNow that we know the slope of the line, we can write the equation of the line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. From the graph, we know that the line passes through the point (0,2), which means the y-intercept (b) is 2.Equation of the line: position = (slope × time) + y-intercept = (3 × time) + 2To find the position at 4 seconds, plug in the time (t = 4 seconds) into the equation:Position at 4 seconds = (3 × 4) + 2 = 12 + 2 = 14Answer: The object was at 14 meters at 4 seconds.