Page 91 - Understanding NCERT Science 09

In this case, the velocity-time graph for the
motion of the car is shown in Fig. 7.6. The
nature of the graph shows that velocity
changes by equal amounts in equal intervals
of time. Thus, for all uniformly accelerated
motion, the velocity-time graph is a
straight line.

–1 )
Velocity (km h

Fig. 7.7: Velocity-time graphs of an object in non-
uniformly accelerated motion.
Fig. 7.7(a) shows a velocity-time graph that
Fig. 7.6: Velocity-time graph for a car moving with represents the motion of an object whose
uniform accelerations. velocity is decreasing with time while
Fig. 7.7 (b) shows the velocity-time graph
You can also determine the distance representing the non-uniform variation of
moved by the car from its velocity-time graph. velocity of the object with time. Try to interpret
The area under the velocity-time graph gives these graphs.
the distance (magnitude of displacement) Activity ______________ 7.9
moved by the car in a given interval of time.
If the car would have been moving with • The times of arrival and departure of
uniform velocity, the distance travelled by it a train at three stations A, B and C
would be represented by the area ABCD and the distance of stations B and C
from station A are given in Table 7.4.
under the graph (Fig. 7.6). Since the
magnitude of the velocity of the car is Table 7.4: Distances of stations B
changing due to acceleration, the distance s and C from A and times of arrival
travelled by the car will be given by the area and departure of the train
ABCDE under the velocity-time graph
(Fig. 7.6). Station Distance Time of Time of
That is, from A arrival departure
s = area ABCDE (km) (hours) (hours)
= area of the rectangle ABCD + area of A 0 08:00 08:15
the triangle ADE
B 120 11:15 11:30
1 C 180 13:00 13:15
= AB × BC + (AD × DE)
2
• Plot and interpret the distance-time
In the case of non-uniformly accelerated
graph for the train assuming that its
motion, velocity-time graphs can have any motion between any two stations is
shape. uniform.

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