Instantaneous change in direction
In a Facebook physics educator group, a member asked the following question:
First time physics teacher here with a graphing question- What would a velocity vs time graph look like if a car was to change direction without slowing down? I got this question and was not able to answer it. Thanks for your help!
This raised a good conversation about this frequent scenario in physics classes. The reality if that this can never actually happen. There must be a short time interval while the force is applied to change the object’s velocity and momentum.
Let’s say, for example, you are driving along a road and a mosquito flying towards you at 2 m/s collides with you and sticks to the windscreen. You are moving -20 m/s. Let’s assume the collision lasts 0.02 seconds. Since you have so much more mass than the mosquito, you barely feel the collision, but the poor mosquito has an acceleration of -1,100 m/s/s (from 2 to -20 m/s in 0.02 s)
This problem is often presented using a vertical line to shift from the positive velocity to the negative. But let’s zoom in on small 2/100ths of a second. Click the arrows to move forward and ‘zoom in’ on the graph:
As you can see, as we zoom in on the moment of collision, the actual slope of the acceleration begins to appear.
In reality, however, even the acceleration line shown in green would not be a straight line, as the force applied to the mosquito would be changing as the bug is compressed into the windscreen.
So, do I have an answer for the question? The reality is no, I don’t. Certain tests will expect you to draw the graph using a vertical line, and to some degree that’s fine. I just hope that my graph above helps folks to better understand the meaning of a ‘vertical’ line on a velocity/time graph.
