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7.4 Graphical Representation of distance travelled by the object is directly
proportional to time taken. Thus, for uniform
Motion speed, a graph of distance travelled against
time is a straight line, as shown in Fig. 7.3.
Graphs provide a convenient method to The portion OB of the graph shows that the
present basic information about a variety of distance is increasing at a uniform rate. Note
events. For example, in the telecast of a that, you can also use the term uniform
one-day cricket match, vertical bar graphs velocity in place of uniform speed if you take
show the run rate of a team in each over. As the magnitude of displacement equal to the
you have studied in mathematics, a straight distance travelled by the object along the
line graph helps in solving a linear equation y-axis.
having two variables. We can use the distance-time graph to
To describe the motion of an object, we determine the speed of an object. To do so,
can use line graphs. In this case, line graphs consider a small part AB of the distance-time
show dependence of one physical quantity, graph shown in Fig 7.3. Draw a line parallel
such as distance or velocity, on another to the x-axis from point A and another line
quantity, such as time. parallel to the y-axis from point B. These two
lines meet each other at point C to form a
7.4.1 DISTANCE–TIME GRAPHS triangle ABC. Now, on the graph, AC denotes
the time interval (t – t ) while BC corresponds
The change in the position of an object with to the distance (s – s ). We can see from the
1
2
1
2
time can be represented on the distance-time graph that as the object moves from the point
graph adopting a convenient scale of choice. A to B, it covers a distance (s – s ) in time
In this graph, time is taken along the x–axis (t – t ). The speed, v of the object, therefore
1
2
and distance is taken along the y-axis. 2 1
can be represented as
Distance-time graphs can be employed under
various conditions where objects move with s 2 – s 1
uniform speed, non-uniform speed, remain v = (7.4)
t – t
at rest etc. 2 1
We can also plot the distance-time graph
for accelerated motion. Table 7.2 shows the
distance travelled by a car in a time interval
of two seconds.
Table 7.2: Distance travelled by a
car at regular time intervals
Time in seconds Distance in metres
0 0
2 1
4 4
Fig. 7.3: Distance-time graph of an object moving 6 9
with uniform speed
8 16
We know that when an object travels equal 10 25
distances in equal intervals of time, it moves
with uniform speed. This shows that the 12 36
78 SCIENCE
Rationalised 2023-24
