Chapter 3, Problem 82A

To determine

The velocity time graph of the each given graph.

Answer to Problem 82A

The velocity time graphs of the given position time graphs are shown in the figure (1), figure (2) and figure (3).

Explanation of Solution

Introduction:

The slope of the position graph describes the velocity of the object. It is same as the first derivative of the equation.

The first graph shows a equation of parabola. The first derivative of the equation of the parabola gives the straight line, so the graph of the velocity time graph becomes a graph of the straight line passing through the origin.

The velocity time graph of the first position time graph is given below in the figure (1).

  

Figure (1)

The position time graph of the second graph shows a straight line. The derivative of the equation of straight line gives the constant slope along the time axis. The velocity time graph of the second position time graph is given below in the figure (2).

  

Figure (2)

The velocity time graph of the third position time graph is given below in the figure (3).

  

Figure (3)

Conclusion:

Thus, the velocity time graphs of the given position time graphs are shown in the figure (1), figure (2) and figure (3).