Suggest a suitable physical situation for each of the following graphs (Fig 2.12):
A police van moving on a highway with a speed of
30 km h–1 fires a bullet at a thief’s car speeding away in
the same direction with a speed of 192 km h–1. If the muzzle
speed of the bullet is 150 m s–1, with what speed does the
bullet hit the thief’s car ? (Note: Obtain that speed which
is relevant for damaging the thief’s car).
Figure 2.11shows the x-t plot of one-
dimensional motion of a particle. Is it correct
to say from the graph that the particle moves
in a straight line for t < 0 and on a parabolic
path for t >0 ? If not, suggest a suitable physical
context for this graph.
Look at the graphs (a) to (d) (Fig. 2.10) carefully
and state, with reasons, which of these cannot
possibly represent one-dimensional motion of
a particle.
In Exercises 2.9 and 2.10, we have
carefully distinguished between
average speed and magnitude of average
velocity. No such distinction is necessary when
we consider instantaneous speed and
magnitude of velocity. The instantaneous speed
is always equal to the magnitude of
instantaneous velocity. Why?
A man walks on a straight road from
his home to a market 2.5 km away with
a speed of 5 km h–1. Finding the
market closed, he instantly turns and
walks back home with a speed of 7.5
km h–1. What is the
(a) magnitude of average velocity, and
(b) average speed of the man over the
interval of time (i) 0 to 30 min, (ii)
0 to 50 min, (iii) 0 to 40 min ?
[Note: You will appreciate from this
exercise why it is better to define
average speed as total path length
divided by time, and not as
magnitude of average velocity. You
would not like to tell the tired man
on his return home that his
average speed was zero !]
Explain clearly, with examples, the distinction between :
(a) magnitude of displacement (sometimes called distance) over an interval of time,
and the total length of path covered by a particle over the same interval;
(b) magnitude of average velocity over an interval of time, and the average speed
over the same interval. [Average speed of a particle over an interval of time is
defined as the total path length divided by the time interval]. Show in both (a)
and (b) that the second quantity
is either greater than or equal to
the first. When is the equality sign
true ? [For simplicity, consider
one-dimensional motion only].
A ball is dropped from a height of 90 m on a floor. At each collision with the floor,
the ball loses one tenth of its speed. Plot the speed-time graph of its motion
between t = 0 to 12 s.
Read each statement below carefully and state with reasons and examples, if it is
true or false ;
A particle in one-dimensional motion
(a) with zero speed at an instant may have non-zero acceleration at that instant
(b) with zero speed may have non-zero velocity,
(c) with constant speed must have zero acceleration,
(d) with positive value of acceleration must be speeding up.
A player throws a ball upwards with an initial speed of 29.4 m s–1
.
(a) What is the direction of acceleration during the upward motion of the ball ?
(b) What are the velocity and acceleration of the ball at the highest point of its motion ?
(c) Choose the x = 0 m and t = 0 s to be the location and time of the ball at its
highest point, vertically downward direction to be the positive direction of
x-axis, and give the signs of position, velocity and acceleration of the ball
during its upward, and downward motion.
(d) To what height does the ball rise and after how long does the ball return to the
player’s hands ? (Take g = 9.8 m s–2 and neglect air resistance).
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