Time is the one thing that can be used directly in both the x and y equations.everything else (displacement, velocity, and acceleration) has to be split into components. This is because everything else is a vector (or a component of a vector, if you'd rather look at it that way), but time is a scalar. One thing to notice is that the t, time, is the only thing that doesn't involve an x or a y. These equations use Dx and Dy for the x and y components of the displacement, rather than the x and y used by the book. Note that these differ from the equations the book uses. These four x equations relate the x-components, while the four y equations relate the y components. If we focus on two dimensions, we get 4 equations for the x direction and 4 more for the y direction. The fact that they are vectors comes in, however, with positive and negative signs. the equations are vector equations, but the variables are not normally written in bold letters.Like the 1D equations, these apply under the following conditions: When the acceleration is constant, we can write out 4 equations that we can use to relate the displacement, initial velocity, velocity, acceleration, and time for each dimension. The instantaneous velocity is given by a similar formula, with the condition that a very small time interval is used to measure the displacement.Ī similar formula gives the average acceleration:Īgain, the instantaneous acceleration is found by measuring the change in velocity over a small time interval. In general, the average velocity will be given by: The velocity will still be represented by v and the acceleration by a. When we're dealing with more than 1 dimension (and we'll focus on 2D, but we could use these same equations for 3D), the position is represented by the vector r. We're going to do the same thing in 2 dimensions, and the equations will look similar this shouldn't be surprising because, as we will see, a two (or three) dimensional problem can always be broken down into two (or three) 1-dimensional problems. In 1 dimension, we wrote down some general equations relating velocity to displacement, and relating acceleration to the change in velocity, and we also wrote down the four equations that apply in the special case where the acceleration is constant. Relevant sections in the book : 3.1, 3.2, and 3.3
0 Comments
Leave a Reply. |