Question

introduction to position-time graphs
position-time graphs tell you where an object is located over a period of time. the slope of the graph tells you how fast the object is moving.

the sign of the slope indicates direction of motion. what would a graph look like if an object is...
moving away from 0 meters
stopped
moving towards 0 meters.

the steepness of the line indicates how fast an object is moving. what would a graph look like if an object is...
moving slowly away from 0 m.
moving quickly away from 0 m.
moving slowly towards 0 m.

if an object’s motion changes, the slope of the line changes. what would a graph look like if an object is...
moves slowly then quickly away from 0 m.
moves quickly towards 0 m, then stops.
is not moving, then moves slowly towards 0 m.

practice: answer the following questions using the graphs

position-time graph
chart: position (m) vs time (s), from (0,0) to (10, ~20)

1. when time increases, what happens to the distance?
2. describe the object’s motion.
3. what is the velocity of the object?

position-time graph
chart: position (m) vs time (s), from (0,20) to (10, 0)

1. when time increases, what happens to the distance?
2. describe the object’s motion.
3. what is the velocity of the object?

Explanation:

Question 1

Step1: Analyze the first graph

The first position - time graph has a positive slope. As time (x - axis) increases, the position (y - axis) values are increasing.

Step2: Conclude the relationship

From the graph, when time (in seconds) increases, the distance (position in meters) also increases.

Step1: Observe the graph's slope

The first position - time graph is a straight line with a positive slope. A straight line in a position - time graph means constant velocity. The positive slope indicates motion away from the origin (0 meters).

Step2: Describe the motion

Since the slope is constant, the object is moving at a constant speed. And because the slope is positive, it is moving away from 0 meters.

Step1: Recall the formula for velocity

Velocity \(v=\frac{\Delta x}{\Delta t}\), where \(\Delta x\) is the change in position and \(\Delta t\) is the change in time.

Step2: Find two points on the graph

From the first graph, at \(t = 0\) s, \(x=0\) m; at \(t = 10\) s, \(x = 20\) m.

Step3: Calculate the velocity

\(\Delta x=20 - 0=20\) m, \(\Delta t = 10-0 = 10\) s. Then \(v=\frac{20}{10}=2\) m/s.

Answer:

When time increases, the distance (position) increases.

Question 2