(a) Draw a graph of s(t) on the t − y plane and restrict t to only vary from 0 to 2. Label axes, units, and your graph.

Question

3. Recall the model rocket with position function s(t) = −16t 2 + 200t from Exercise 2. 

 (a) Draw a graph of s(t) on the t − y plane and restrict t to only vary from 0 to 2. Label axes, units, and your graph.  

This is exercise 2 to help draw the graph

You launch a model rocket into the air with an initial speed of 200 feet per second. The position of the rocket is given by the function s(t) = −16t^2 + 200t, where t is in seconds, and s(t) in feet. 

 (a) Compute the average velocity on the interval t ∈ [1, 1.5].  

At t=1 s(t)= s (1) = -16(1) ^2 +200(1) =184; At t=1.5 s (1.5) =264; 264-184/1.5-1 avg velocity= 160m/s 

(b) Compute the average velocity on the interval t ∈ [1, 1.1].  

S (1.1) =-16(1.1) ^2+ 200(1.1) = 200.64; 200.64-184/1.1-1 avg velocity = 166.4 m/s 

(c) Compute the average velocity on the interval t ∈ [1, 1.01]. 

S (1.01) = -16(1.01) ^2+200(1.01) = 185.7; 185.7-184/1.01-1 avg velocity= 167.84 

 (d) Notice that in parts (a) through (c), although we are still computing average velocities, the time interval over which we are finding the average velocity is becoming smaller and smaller. That is, the interval is getting closer and closer to a single instant, specifically, the time t = 1. Using this fact and the answers from (a) through (c) above, estimate what you expect the instantaneous velocity of the rocket is at the time t = 1.  

 -16(t)^2+200(t)-(-16+200)/t-1 = -16(t-1) ^200(t-1)/t-1 = -16(1+1) +200; v1 at t=1 = 168 

Answer 1

I believe where you are having concern is the "restrict t to only vary between 0 to 2".

Some graphing calculators or websites make it difficult to do such a thing.

This is not the case with an application I trust called GeoGebra. As the name sort of implies, it excels basically everything Geometry and Algebra (and even further into Calculus and such). I recommend GeoGebra Classic as that has everything to consider when working with 2-D sketches that you're working with. Other GeoGebra versions exist for 3-D but that's another app for another day.

If you input the function (legitimately type the following as is):

s(t) = 200 * t - 16 * t^2

And ask it to plot it (by hitting Enter on your keyboard), it will display the entire output of that function from -∞ to +∞.

To restrict it, the developers made a very convenient way to do so. They created a function called Function (very creative, I know). Type Function(s,0,2) into the input area and hit Enter to confirm what you just typed. How Function works is that you tell it what equation you want to restrict, give it a starting x (for you, a starting t) value and then a ending x (again, for you, an ending t) value. The bounds of the displayed graph will be off because the Home Zoom area is quite tiny and the results of this function are quite large.

Going into the settings, redefining the x and y limits until the graph area has the full plot you are looking for should fulfill what the question is asking for.

They are other settings found inside this app that allow you to apply units to the x and y (for you, t and s) axes.

Let me know if there is anything else I can help you with.