Q4Q - Fundamentals Of Physics

Question

Figure 2-19 is a graph of a particle’s position along an x axis versus time. (a) At time$\mathit{t}\mathbf{=}\mathbf{0}$, what is the sign of the particle’s position? Is the particle’s velocity positive, negative, or 0 at (b)$\mathit{t}\mathbf{=}\mathbf{1}\mathbf{ }\mathit{s}$, (c)$\mathit{t}\mathbf{=}\mathbf{2}\mathbf{ }\mathbf{s}$, and (d)$\mathit{t}\mathbf{=}\mathbf{3}\mathbf{ }\mathbf{s}$? (e) How many times does the particle go through the point$\mathbf{x}\mathbf{=}\mathbf{0}$?

Step-by-Step Solution

Answer

(a) Position is negative

(b) Velocity is positive at t=1 s

(c) Velocity is zero at t =2 s

(d) Velocity is negative at t =3 s

(e) Particle goes through the point x=0 twice at t =1 s and t =3 s 

Step 1: Given information

The graph in figure 2.19

Step 2: To understand the concept

The velocity is the rate of change of displacement. If the displacement for the given time interval is positive, the velocity is also positive, if the displacement is negative the velocity is negative. The velocity is also equal to the slope of displacement vs the time graph.

Step 3: (a) To find the particle’s sign of position

From the given graph it is seen that when t =0, the position of the particle is below the time axis. It means the position is on the negative axis of the position. Thus, the position of the particle at t =0 is negative

Step 4: (b) To find the particle’s velocity at t = 1   s

The velocity of the particle is given by,

$\overrightarrow{v}=\frac{d\overrightarrow{x}}{dt}$

The expression also represents the slope of the graph. Now, if the slope is positive, it can be concluded that the velocity is positive. If the slope is negative, it can be concluded that the velocity is negative. And, if the slope is zero, it can be concluded that the velocity is zero.

 

From the graph, it can be seen that the slope is positive. Thus, the velocity of the particle at t =1 is positive.

Step 5: (c) To find the particle’s velocity at t =2 s

The slope of x versus t is zero.

Thus, the velocity of the particle at t=2 s is zero

Step 6: (d) To find the particle’s velocity at t =3 s

From the graph, it can be seen that the slope of x versus t is negative.

 

Thus, the velocity of the particle at t =3 s is negative.

Step 7: (e) How many times do particles go through the point x =0

From the graph, it can be seen that the particle goes through the point x=0 twice at t =1 s and t =3 s