lesson 4 describing motion with position vs. time...

Name: _________________________ Physics 11 Honours Blk: _________

Lesson 4 Describing Motion with Position vs. Time Graphs

A person walking along a straight line is being timed while their position from the starting point is

recorded. The data is recorded in the following table:

Time (s) 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00

Distance

(m)

4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0

Graph the data below:

a) What is the y intercept of this graph?

b) What is the slope of this graph?

c) What is the equation of this graph?

Key Idea: The slope of a displacement vs time graph is the velocity, What if we have a changing

velocity? Ex. 2) Describe what is happening over each interval of the distance vs time graph below:

a) Find the average speed over each interval:


b) What is the average velocity for the entire trip?

c) What is the average speed for the entire trip?

Average Slope vs Instantaneous Slope

Constant Velocity

Positive Velocity

Positive Velocity

Changing Velocity (acceleration)

Slow, Rightward(+) Constant Velocity

Fast, Rightward(+) Constant Velocity


0.5 1.0 1.5 2.0 2.5

Dis

tance

km

0

5

10

15

20

25

So, we can use this approach to approximate the slope of a curve in order to find the instantaneous

velocity. Graph of distance Vs time

35

30

Time (h)


a) Find the instantaneous velocity for every 30 minute interval on the graph above. Clearly show

the line that you used to calculate the instantaneous slope on the graph, and show your

calculations for the slope as well.

b) At what time(s) has this person come to a stop?

Negative (-) Velocity

Slow to Fast

Leftward (-) Velocity

Fast to Slow

Check Your Understanding

1- Use the principle of slope to describe the motion of the objects depicted by the two plots below

2. Determine the velocity (i.e., slope) of the object as portrayed by the graph below. When you believe

you know the answer (and not before), click the button to check it.

3. The graph below represents the displacement of an object moving in a straight line as a

function of time. What was the total distance traveled by the object during the 10-second time

interval?


a. What is velocity of the object moving in this graph at 4 seconds?

b. What is the velocity of the object moving in this graph at 6 seconds?

c. What is the velocity of the object moving in this graph at 10 seconds?

d. How far did this object in this graph go in 5 seconds?

e. What is the average SPEED of this object after 15 seconds?

f. What is the total displacement after 15 seconds?

g. What is the average VELOCITY of this entire graph's motion. Answer in a fraction

5. A high-speed train in Japan travels a distance of 300 kilometers in 3.60 × 103

seconds. What is the

average speed of this train?

a. 1.20 × 10-2 m/s b. 8.33 × 10-2 m/s c. 12.0 m/s d. 83.3 m/s

6. A child walks 5 meters north, then 4 meters east, and finally 2 meters south. What is the magnitude of the

resultant displacement of the child after the entire walk?

7. A car travels 90 meters due north in 15 seconds. Then the car turns around and travels 40 meters due

south in 5 seconds. What is the magnitude of the average velocity of the car during this 20-second

interval?


Lesson #4 - Worksheet Distance-Time Graphs

Examine this graph carefully to answer questions 1 and 2.

1. How far is the truck from its starting point after:

(a) 10 s (b) 15 s (c) 30 s

(d) 43 s (e) 50 s

2. What is the truck’s velocity in each of the intervals A through E?

3. Beside the graph, describe briefly the kind of motion that is taking place in each of the

situations represented by the following displacement vs. time graphs.

4. Beside the graph, describe briefly the motions represented by each of these graphs. If

the speed is changing, state whether it is increasing or decreasing.


5. Beside the graph, describe the motion represented by each of the following displacement

vs. time graphs.

Use the following graph for question 6.

6. a) From the graph above, calculate the average speed for the entire 22 s.

b) Find the average speed for each of the following time intervals:

(i) 0 s to 2 s (ii) 4 s to 8 s

(iii) 14 s to 18 s (iv) 6 s to 17 s

c) Find the instantaneous speed at (i) 12 s (ii) 16 s

lesson 4 describing motion with position vs. time...

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