Question

problem 2. observe the following plot of an objects position across time.
answer the following three questions:

1. describe in one full sentence the motion of this object.
2. what is the objects velocity at ( t = 3s )?
3. what is the objects acceleration?

Explanation:

Step1: Analyze the motion from the graph

The position - time graph is a straight line, which means the object is moving with a constant velocity.

Step2: Calculate the velocity

The formula for velocity from a position - time graph is \(v=\frac{\Delta x}{\Delta t}\). Taking two points on the line, say \((0,0)\) and \((6,14)\), \(\Delta x = 14 - 0=14\space m\) and \(\Delta t=6 - 0 = 6\space s\). But we can also use the slope formula. The general form of a straight line is \(y = mx + c\), in position - time \(x=vt+x_0\) (where \(x_0 = 0\) here). The slope \(m = v\). Using the formula \(v=\frac{x_2 - x_1}{t_2 - t_1}\), if we take \(x_1 = 0,t_1 = 0\) and \(x_2=14,t_2 = 6\), \(v=\frac{14 - 0}{6-0}=\frac{7}{3}\space m/s\approx2.33\space m/s\). Since the motion is uniform (straight - line graph), the velocity at \(t = 3s\) is the same as the average velocity.

Step3: Determine the acceleration

The formula for acceleration is \(a=\frac{\Delta v}{\Delta t}\). Since \(v\) is constant (straight - line position - time graph implies constant \(v\)), \(\Delta v=0\). So, \(a = 0\space m/s^{2}\)

Answer:

1. The object is moving with a constant velocity.
2. The object's velocity at \(t = 3s\) is \(\frac{7}{3}\space m/s\approx2.33\space m/s\)
3. The object's acceleration is \(0\space m/s^{2}\)