Question

interpreting a position vs. time graph
use the graph to determine the velocity of the object.
what is the instantaneous velocity of the object at 3
seconds?
m/s
what is the average velocity of the object?
m/s

Explanation:

Step1: Determine instantaneous velocity at \(t = 3s\)

On a position - time graph, the slope of the tangent line gives the instantaneous velocity. At \(t = 3s\), the graph is in the rising - straight - line part. The formula for slope \(m=\frac{\Delta x}{\Delta t}\). For the rising part, \(x_1 = 0\) at \(t_1=0\) and \(x_2 = 12\) at \(t_2 = 4\). So \(v=\frac{12 - 0}{4-0}=3\) \(m/s\).

Step2: Calculate average velocity

The formula for average velocity is \(v_{avg}=\frac{\Delta x_{total}}{\Delta t_{total}}\). The total displacement \(\Delta x_{total}=0\) (starts at \(x = 0\) and ends at \(x = 0\)), and the total time \(\Delta t_{total}=12s\). So \(v_{avg}=\frac{0}{12}=0\) \(m/s\).

Answer:

The instantaneous velocity at \(3\) seconds is \(3\) \(m/s\). The average velocity is \(0\) \(m/s\).