(a) Sketch a graph of velocity versus time corresponding to the graph of displacement versus time given in Figure 2.55.

(b) Identify the time or times ( ta , tb , tc , etc.) at which the instantaneous velocity is greatest.

(c) At which times is it zero?

(d) At which times is it negative?

The velocity vs. time graph we get when we take the slope of the displacement versus time graph.

The slop of this graph gives the value of the velocity, and it also determines the direction of the velocity

$\mathbf{V}\mathbf{=}\mathbf{tan\theta }$

If we try to draw the slop on the given point, we will get a similar figure :

Figure: The slope of the graph at given points

a. Hence we can try to plot the graph using this given data :

(b)

The time at which instantaneous velocity is greatest is t_d as the maximum value of the velocity is seen at time td.

(c)

Using the above slops in the graph, we can plot the value of velocity. When the slop is horizontal, velocity is ZERO.

When the slop is vertical, the slope increases to infinite hence velocity will also be infinite.

Instantaneous velocity is zero at t_c, t_e, t_g, t_l because, at this point, the graph is touching the x-axis that, is the value of the velocity is becoming zero at this point.

(d)

The velocity is negative at t_a, t_b, and t_f. because at this point, the graph has a negative value of the velocity