Question

Figure 5-25 gives three graphs of velocity component and three graphs of velocity component . The graphs are not to scale. Which graph and which graph best correspond to each of the four situations in Question 1 and Fig. 5-19?

Short answer

1. Graph ‘a’ of ${\mathrm{V}}_{\mathrm{x}}$corresponds to case 1 of figure 5.19.
2. Graph ‘b’ of ${\mathrm{V}}_{\mathrm{x}}$corresponds to case 3 of figure 5.19.
3. Graph ‘c’ of ${\mathrm{V}}_{\mathrm{x}}$corresponds to cases 2 and 4 of figure 5.19.
4. Graph ‘d’ of ${\mathrm{V}}_{\mathrm{y}}$corresponds to case 2 of figure 5.19.
5. Graph ‘e’ of${\mathrm{V}}_{\mathrm{y}}$corresponds to case 1 of figure 5.19
6. Graph ‘f’ of${\mathrm{V}}_{\mathrm{y}}$corresponds to case 3 and case 4 of figure 5.19

Step-by-step solution

Given information

The graph is given in figure 5-25

To understand the concept

We can calculate the velocity of an object from the graph of force by assuming the mass value as constant.

(a) To graph a of Vx corresponds to case 1 of figure 5.19

Graph ‘a’

Velocity component V_x is constant for the given values of the time. It means the acceleration for an object and hence the x component of force is zero. This is case 1 of figure 5.19, as in that figure forces on the x-axis get canceled out.

(b) graph a of Vx corresponds to case 3 of figure 5.19

Graph ‘b’

This graph shows that the value of V_x is increasing with time. So, this graph corresponds to case 3, as in this case, the force component along x is negative.

(c) To graph a of Vx corresponds to cases 2 and 4 of figure 5.19

Graph ‘c’

This graph shows the velocity V_x increasing in the negative direction. So, this graph corresponds to cases 2 and 4.

(d) To graph a of Vx corresponds to case 2 of figure 5.19

Graph ‘d’

This graph has a constant value for the y component of velocity. So, this corresponds to case 2.

(e) To graph a of Vx corresponds to case 1 of figure 5.19

Graph ‘e’

This graph shows the V_y values are increasing with time t. Hence, it corresponds to case 1.

(f) To graph a of Vx corresponds to cases 3 and 4 of figure 5.19

Graph ‘f’

This graph shows the V_y component increasing in a negative direction. Hence, it corresponds to case 3 and case 4.