Question

1. what is the speed in the first 2 seconds?
2. what is the speed between 4 seconds and 6 seconds?
3. what is the average speed of the object represented on the graph?

Explanation:

Step1: Calculate speed in the first 2 seconds

Speed formula: \(v=\frac{\Delta d}{\Delta t}\). From the graph, at \(t = 0\), \(d=0\); at \(t = 2\), \(d = 2\). So \(\Delta d=2 - 0=2\) m, \(\Delta t=2 - 0 = 2\) s. Then \(v=\frac{2}{2}=1\) m/s.

Step2: Calculate speed between 4 - 6 seconds

At \(t = 4\), \(d = 3\); at \(t = 6\), \(d = 3\). \(\Delta d=3 - 3=0\) m, \(\Delta t=6 - 4 = 2\) s. Using \(v=\frac{\Delta d}{\Delta t}\), \(v=\frac{0}{2}=0\) m/s.

Step3: Calculate average speed

Average speed formula: \(v_{avg}=\frac{d_{total}}{t_{total}}\). From the graph, \(d_{total}=8\) m (at \(t = 12\) s), \(t_{total}=12\) s. So \(v_{avg}=\frac{8}{12}=\frac{2}{3}\approx0.67\) m/s.

Answer:

1. \(1\) m/s
2. \(0\) m/s
3. \(\frac{2}{3}\approx0.67\) m/s