| Problem statement Solution video |
DISCUSSION THREAD
Ask and answer questions here. You learn both ways.
Discussion
Consider the animation below of the motion for particle P:
- For all time, P moves with a positive x-component and a negative y-component of both velocity and acceleration. Why? Can you see this in the animation?
- As we will see in the next class period when we talk about the "path description" of kinematics, the velocity of a point is always tangent to the path of the point, and the acceleration always points "inward" on the path of the point. Do you see this in the animation?
The components of velocity and acceleration of P are found directly from the time derivatives of the position components:
vP = x_dot i + y_dot j
aP = x_ddot i + y_ddot j
This question is a very straightforward application of what we learned in class today. All you need to do is apply the two fundamental equations we learned.
Should we define the i unit vector in the same direction as x in the figure or the typical direction?
The unit vector i should always point in the positive x-direction. Therefore, if x points to the left, then i should point to the left.
Make sure that when you answer the problem, your answers are in vector form because velocity and acceleration are both vector quantities.
Double check the units as you go. Logically they should change when taking a derivative or integral.
Try not to overcomplicate this problem. Using the x-component and y-component equations of position we can find the vector quantities of velocity and acceleration.