An object’s trajectory can be described by x= (12t3−2t2)m and y=(12t2−2t)m, where t is in seconds. The value of time determines the location on the graph for both x and y. This means that solving one variable will give you the other. We can find the velocity by dividing the distance traveled with time.
Doing so, we get v= √(x₀ + y₀) / t = (√12t²+t)/s or s/sec. Inversely, we can solve for x and y when given a known position on the graph as follows: y=(-xt/(√12))m and x=(-yt/(√12))m. This will give us our starting positions to plot our trajectory again! #endtask_writecontent()” class=”postfooterlink post comment link” title=”” href=”#comments” tabindex=”0″/> notitle>” /> notitle>” /> Euler’s Model of Motion: How Solving for One Determines the Other In this post, I will be exploring how solving one variable in an object’s trajectory can lead you to solving the other. This is a model created by Euler and his equation describes velocity as v= √(x₀ + y₀) / t = (√12t²+t)/s or s/sec. When we solve for x and y from this point graphically, it gives us our starting positions to plot our trajectory again! It is quite simple really; all you need is a pen, paper, your watch with seconds hand and something easily movable like a chair.