Ejs Open source java applet Displacement & Velocity time graph for area & dx/dt

« on: September 22, 2008, » posted from:Singapore,,Singapore

Open source Ejs applet Displacement & Velocity time graph showing relationships of area & dx/dt

http://home.phy.ntnu.edu.tw/~lookang/EJS/EJS_4.0_080905/weexva3/weexva3.html old version

http://home.phy.ntnu.edu.tw/~lookang/EJS/EJS_4.0_080905/weexva4/weexva4.html old

http://home.phy.ntnu.edu.tw/~lookang/EJS/EJS_4.0_080905/weexva10/weexva10.html

http://home.phy.ntnu.edu.tw/~lookang/EJS_4.1_090115/weexva10_Simulation.html

adapted from Two dogs running (set up xi,vi, and a ) http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=188.msg810#msg810

Displacement & Velocity time graph applet showing relationships of area & dx/dt

Aims to show more clearly the ideas usually difficult for students

rate of change in displacement versus time at that time t = velocity at the same time.

Area of velocity versus time graph = distance traveled in Displacement time graph

exercise by lookang

for http://www.seab.gov.sg/oLevel/syllabus/5058_2011.pdf

2. Kinematics

Content

• Speed, velocity and acceleration

• Graphical analysis of motion

• Free-fall

• Effect of air resistance

Learning Outcomes:

Candidates should be able to:

(a) state what is meant by speed and velocity

(b) calculate average speed using distance travelled / time taken

(c) state what is meant by uniform acceleration and calculate the value of an acceleration using

change in velocity / time taken

(d) interpret given examples of non-uniform acceleration

(e) plot and interpret a distance-time graph and a speed-time graph

(f) deduce from the shape of a distance-time graph when a body is:

(i) at rest

(ii) moving with uniform speed

(iii) moving with non-uniform speed

(g) deduce from the shape of a speed-time graph when a body is:

(i) at rest

(ii) moving with uniform speed

(iii) moving with uniform acceleration

(iv) moving with non-uniform acceleration

(h) calculate the area under a speed-time graph to determine the distance traveled for motion with

uniform speed or uniform acceleration

(i) state that the acceleration of free fall for a body near to the Earth is constant and is

approximately 10 m/s2

(j) describe the motion of bodies with constant weight falling with or without air resistance,

including reference to terminal velocity

Prior Knowledge required

nil

Engage

1. How do you predict if the cat or the dog will reach the tree sooner? In physics, is it possible to estimate and predict which of the animal (cat or dog) will reach the tree first. There are some variables which you need to establish in order to predict. Can you list some the variables? Can you think of different ways to reach the tree?

hint: initial velocity vi, initial displacement xi (starting position), acceleration a .....

After some discussions, students can share their ideas through oral/verbal presentation.

Advance Level:

Teacher can praise some of the ideas and point them to Ejs as a means to test (modeling approach) out their ideas using this Ejs simulation codes as templates for implementation.

Beginner Level:

Teacher can introduce the simulation to allow students to learn by experiencing.

Explore

1. Explore the simulation, this simulation is designed with a cat 1 and dog 2 moving in the x direction only between a house x = -100 m to a tree x = 100 m.

2 The play button runs the simulation, click it again to pause and the reset button brings the simulation back to its original state.

3 by default values, play the simulation. Notice that the top motion diagram (world view) shows the cat 1 and dog 2 moving in a straight line in the x direction. What is the physics principle(s) simulated here.Write down what you observe. Explain the motion in terms of the influences of initial displacement, initial velocity and acceleration for the whole motion.

_____________________________________________________________________

hint: newton's 1st law for dog 2 and newton's second law of cat 1

4 write down what does which of the slider represent or control?

for cat 1: x1i=______________, u1 =__________, a1=___________________

dog 2: x2i=_______________, u2=__________, a2=___________________

5 reset the simulation.

6 using the default values (x1i= =-100, u1=0, a1=12) and (x2i= =-100, u2=20, a2=0), play the simulation. write down the time for which the cat 1 reach the tree. ________________

7 select (x1i= =-100, u1=0, a1=0) and (x2i= =-100, u2=20, a2=0) and play the simulation.

write down the time for which the dog 2 reach the tree. ________________

notice that by making u1=0 and a1=0, the cat is stationary.

8 explore the slider x1i, u1, a1. what do these sliders control?

9 explore the slider x2i, u2, a2. what do these sliders control?

10 by leaving the cursor on the slider, tips will appear to give a description of the slider.

11 vary the simulation and get a sense of what it does.

12 reset the simulation and ignore the dog 2 for the steps below

13 predict what the graphs of displacement versus time and velocity versus time will look like for the following cases.

(i) at rest

(ii) moving with uniform speed

(iii) moving with uniform acceleration

*(iv) moving with non-uniform acceleration

14 select suitable values of the cat 1 for each of the cases above.

record down the values you suggested and explain why you choose them.

15 draw the graphs of displacement versus time and velocity versus time on paper with the prediction and observed plots of the cat 1 side by side. Are there any difference(s)? Elaborate on the difference(s) if any and discuss with their classmates. Consult your teacher if you need help.

16 by default values, play the simulation. select the checkboxes x1=x1f-x1i and x2=x2f-x2i at the top menu hint: what is displacement,x? suggest with reason, what is the meaning of displacement in terms of the (i) motion diagram and (ii) x versus t graph?

At the end of the simulation, notice the time slider is drag-gable for further exploration. Is your answer appropriate?

16 by default values, play the simulation. select the checkboxes x1=x1f-x1i and x2=x2f-x2i at the top menu hint: what is distance traveled? suggest with reason, what is the meaning of distance traveled in terms of the (i) motion diagram and (ii) v versus t graph?

17 Elaborate on what is the difference between displacement and distance traveled. You may explore the simulation to test your elaboration, if see if it is robust enough or is there a more precise way to describe them?

H

18 by default values, play the simulation. notice write down at the end of the simulation the values of for the following

displacement of cat 1, x1 = ______________

displacement of dog 2, x2 = ______________

distance traveled by cat 1, d1 = ______________

distance traveled by dog 2, d2= _______________

19 suggest suitable equations for this specific case.

x1 = ______________

x2 = ______________

d1 = ______________

d2= _______________

20 describe how did you arrived at the equation for d1 (cat under uniform acceleration) and d2 (dog under uniform velocity).

Optional:

21 how is dx/dt represented in the (i) motion diagram,(ii) x versus t and (iii) v versus t ?

hint: select checkbox what is dx/dt?

Evaluate:

22 A cat says to the dog "I will start with negative initial velocity and still reach the tree sonner than the dog that is running at constant velocity of 20 m/s" play with the simulation suggest suitable values of initial condition(s) and record systematically, determine if the cat is correct. State your assumptions made.

Have Fun!