Question

assume that you are walking away from a motion sensor that is connected to a computer which will draw a position vs. time graph for your motion. predict (sketch -- either by hand or using a computer program) the position vs. time graph

Explanation:

Step1: Analyze the motion

When walking away from the motion - sensor, the distance (position) from the sensor increases with time.

Step2: Determine the graph shape

The position - time graph will be a straight - line with a positive slope if the walking is at a constant speed. If the speed is not constant, the graph will be a non - linear curve. For a constant speed motion, the position $x$ as a function of time $t$ can be modeled by the equation $x = vt+x_0$, where $v$ is the speed, $t$ is the time and $x_0$ is the initial position. The graph will start at the initial position $x_0$ (when $t = 0$) and will have a positive - sloped line if $v>0$.

Answer:

If walking at a constant speed, a straight - line with a positive slope starting from the initial position. If speed is non - constant, a non - linear curve with a generally increasing trend.