Trace Curve: x(t)=1+t, y(t)=t/2 0-2

In summary, the conversation discusses tracing the functions x(t)= 1+t and y(t)= t/2 as t advances from 0 to 2. The axis in terms of t are described, with positive x at 0 or 2, positive y at 1/2, negative x at 1, and negative y at 1.5. The speaker is unsure of how to trace the functions, but it is suggested to pick values of t and plot the corresponding points to sketch the curve.
  • #1
mattmannmf
172
0
let x(t)= 1+t and y(t)= t/2

trace (x(t),y(t)) as t advances from 0 to 2.

Im just unsure of how to trace it. Is it pretty much the same thing as tracing it from 0 to 2pi except I am leaving out the pi?

So axis in term of t:
positive x= 0 or 2
positive y= 1/2
negative x= 1
negative y= 1.5
 
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  • #2
mattmannmf said:
let x(t)= 1+t and y(t)= t/2

trace (x(t),y(t)) as t advances from 0 to 2.

Im just unsure of how to trace it. Is it pretty much the same thing as tracing it from 0 to 2pi except I am leaving out the pi?

So axis in term of t:
positive x= 0 or 2
positive y= 1/2
negative x= 1
negative y= 1.5

Pick a few values of t (like t=0,1/2,1,etc.) and write down the pairs (x(t),y(t)) for each of them. Plot these points and sketch the curve through them.
 

1. What is a trace curve?

A trace curve is a parametric curve that describes the path of a particle or object in motion. It is represented by two equations, one for the x-coordinate and one for the y-coordinate, both in terms of a third variable t which represents time. In this case, the trace curve is defined by x(t)=1+t and y(t)=t/2 for values of t between 0 and 2.

2. How do you graph a trace curve?

To graph a trace curve, you can plot points by choosing different values for t and plugging them into the equations x(t) and y(t). Then, connect the points with a smooth curve to create the trace curve.

3. What information does a trace curve provide?

A trace curve can provide information about the position, velocity, and acceleration of an object in motion. It can also show the direction and speed of the object at different points along the curve.

4. What does the range of t values represent in a trace curve?

The range of t values in a trace curve represents the time interval for which the object is in motion. In this case, the range of t values is 0 to 2, indicating that the object is in motion for 2 seconds.

5. Are trace curves only used for linear motion?

No, trace curves can represent the motion of objects following any path, not just straight lines. They can also be used to describe the motion of objects in two or three dimensions.

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