# Arizona State University| PHY 121: Univ Physics I: Mechanics|Homework 1-2| Given Positions, Find Velocity and Acceleration

Learning Goal: To understand how to graph position, velocity, and acceleration of an object starting with a table of positions vs. time.

### The table shows the x coordinate of a moving object. The position is tabulated at 1-s intervals. The x coordinate is indicated below each time. You should make the simplification that the acceleration of the object is bounded and contains no spikes.

 time (s) 0 1 2 3 4 5 6 7 8 9 x (m) 0 1 4 9 16 24 32 40 46 48

### PART A. Which of the graph below best represents the function $x(t)$, describing the object’s position vs. time?

A bounded and nonspiky acceleration results in a smooth graph of x vs. t.

### PART B. Which of the following graphs below best represents the function v(t), describing the object’s velocity as a function of time?

The velocity toward the end of motion is positive and decreasing. This narrows the options down to either graph 1 or 4.

Two of the possible velocity vs. time graphs indicate zero velocity between t=4 and t=7s. The implications of the zero velocity means that the position vs. time graph is a horizontal line.

The problem states that “the acceleration of the object is bounded and contains no spikes.” This means that the velocity has no discontinuities.