Exercise 4.7
Once all points are plotted, connect them to create the position-time graph for the vehicle’s motion (Fig. 4.11c). It is a straight line for the data given in Table 4.3. This was an example of plotting a position-time graph. Similar procedure can be used to plot the other graphs which you will be learning ahead. Ready to Go Beyond The intermediate points represent possible values for position of vehicle at intermediate times. They are correct if vehicle is moving with a constant speed. Example : For a vehicle starting from rest and speeding up, the data for position and time are given in Table 4.4. Plot the position-time graph corresponding to it. Answer: Choosing the scale to be X-axis: divisions = s Y-axis: divisions = m and following the procedure of Activity , all points corresponding to positions of the vehicle at different instants of time are marked. Unlike Fig. 4.11c, the points do not fall on a straight line. The points can be joined by a curve as shown in Fig. 4.12. Now that you know how to plot a graph from the data given for the motion of an object, let us learn to interpret the graphs.
Not cross-checked
NCERT prints no numerical answer for this exercise, so this working has not been cross-checked against the book.
Joining the plotted points of Table $\displaystyle 4.3$ gives a straight line passing through the origin (Fig. 4.11c) — the position-time graph of the vehicle.
A straight-line position-time graph means the velocity is constant: the object covers equal displacements in equal intervals of time.
The slope of that line gives the velocity: \(\displaystyle v = \frac{120\ \text{m} - 0\ \text{m}}{6\ \text{s} - 0\ \text{s}} = 20\ \text{m s}^{-1} \).
The points between the plotted ones stand for genuine positions at in-between instants only because the vehicle is moving at a constant speed.
Contrast with Example $\displaystyle 4.5$ (Table $\displaystyle 4.4$): there the points do not fall on a straight line and are joined by a curve (Fig. $\displaystyle 4.12$), which means the velocity is changing — accelerated motion.