Question

what is the instantaneous velocity at 1.5 * seconds? position vs. time 30 24 18 12 6 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 time (s) 3 m/s 1.6 m/s 4 m/s 6.0 m/s 4.4 m/s

Explanation:

Step1: Recall velocity - position relationship

Velocity is the slope of the position - time graph. For a linear part of the position - time graph, the instantaneous velocity is equal to the average velocity.

Step2: Select two points on the linear part

For \(t = 0\ s\), \(y = 0\ m\) and for \(t = 6\ s\), \(y=24\ m\) (the graph is linear from \(t = 0\ s\) to \(t = 6\ s\)).

Step3: Calculate the slope

The slope \(v=\frac{\Delta y}{\Delta t}\), where \(\Delta y=y_2 - y_1\) and \(\Delta t=t_2 - t_1\). So \(v=\frac{24 - 0}{6 - 0}\).
\[v=\frac{24}{6}=4\ m/s\]
Since the motion is linear from \(t = 0\ s\) to \(t = 6\ s\), the instantaneous velocity at \(t = 1.5\ s\) is the same as the average velocity of this linear part.

Answer:

C. 4 m/s