In Fig. 2-44, (a) during what time periods, if any, is the velocity constant? (b) At what time is the velocity greatest? (c) At what time, if any, is the velocity zero? (d) Does the object move in one direction or in both directions during the time shown?

Figure 2-44 Problems 57,58 and 59

The graph plotted between the position of an object and the time taken is referred to as the position-time graph. You can measure the velocity with the help of this graph. The slope of the position-time graph at any point gives the velocity of the object at that point.

The velocity of an object is constant, where the slope of the position-time graph is constant. It is equivalent to the time period in which the position of the object varies at a constant rate with respect to time.

The graph is straight from t = 0 s to t = 22 s, approximately. Thus, the slope of the graph and the velocity of the object are constant between t = 0 s and t = 22 s.

The slope of the position-time graph gives the velocity. The velocity of an object is the greatest when the positive slope of the graph is the largest (or steepest).

The slope of the given graph is the steepest between 22s and 29s. Thus, in this duration, the velocity of the object is the greatest.

The velocity of an object is zero when the position-time graph is parallel to the time axis, i.e.,whentheposition of the object does not change with time.

The graph is at its peak between 35 s and 40 s. In this time interval, the velocity of the object becomes zero for a moment at the peak as the tangent to the graph for this duration becomes parallel to the time axis.

Thus, the velocity of the rabbit is zero at t = 37 s.

The slope of the graph remains positive up to t= 37 s and becomes negative after this time. The displacement of the object increases till it reaches approximately 20 m at t= 37 s and then decreases. Therefore, the object moves in both directions and changes its direction after t= 37 s.