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**Exercise : ** Solutions of Questions on Page Number : **55**

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Q1 :
**
**

In which of the following examples of motion, can the body be considered approximately a point object:

(a) a railway carriage moving without jerks between two stations.

(b) a monkey sitting on top of a man cycling smoothly on a circular track.

(c) a spinning cricket ball that turns sharply on hitting the ground.

(d) a tumbling beaker that has slipped off the edge of a table.

**Answer :**

**Answer:** (a), (b)

**(a)** The size of a carriage is very small as compared to
the distance between two stations. Therefore, the carriage can be
treated as a point sized object.

**(b)** The size of a monkey is very small as compared to the
size of a circular track. Therefore, the monkey can be considered
as a point sized object on the track.

**(c)** The size of a spinning cricket ball is comparable to
the distance through which it turns sharply on hitting the
ground. Hence, the cricket ball cannot be considered as a point
object.

**(d)** The size of a beaker is comparable to the height of
the table from which it slipped. Hence, the beaker cannot be
considered as a point object.

Answer needs Correction? Click Here

Q2 :
**
**

The position-time (*x-t*) graphs for two children A and B
returning from their school O to their homes P and Q respectively
are shown in Fig. 3.19. Choose the correct entries in the
brackets below;

(a) (A/B) lives closer to the school than (B/A)

(b) (A/B) starts from the school earlier than (B/A)

(c) (A/B) walks faster than (B/A)

(d) A and B reach home at the (same/different) time

(e) (A/B) overtakes (B/A) on the road (once/twice).

**Answer :**

**Answer:**

**(a) A** lives closer to school than **B.**

**(b) A** starts from school earlier than **B.**

**(c) B** walks faster than **A.**

**(d) A** and **B** reach home at the same time.

**(e) B** overtakes **A** once on the road.

**Explanation:**

**(a)** In the given *x*-*t*
graph, it can be observed that distance OP < OQ. Hence, the
distance of school from the
**A's**
home is less than that from
**B's**
home.

**(b)** In the given graph, it can be observed that for
*x* = 0, *t* = 0 for **A**, whereas for *x* =
0, *t* has some finite value for **B**. Thus, **A**
starts his journey from school earlier than **B**.

**(c)** In the given *x*-*t*
graph, it can be observed that the slope of **B** is greater
than that of **A**. Since the slope of the
*x*-*t* graph gives the speed, a
greater slope means that the speed of **B** is greater than
the speed **A**.

**(d)** It is clear from the given graph that both **A**
and **B** reach their respective homes at the same time.

**(e)** **B** moves later than **A** and his/her speed
is greater than that of **A.** From the graph, it is clear
that **B** overtakes **A** only once on the road.

Answer needs Correction? Click Here

Q3 :
**
**

A woman starts from her home at 9.00 am, walks with a speed of 5
km h^{-1} on a straight road up to
her office 2.5 km away, stays at the office up to 5.00 pm, and
returns home by an auto with a speed of 25 km
h^{-1}. Choose suitable scales and
plot the *x*-*t* graph of her motion.

**Answer :**

Q4 :
**
**

A drunkard walking in a narrow lane takes 5 steps forward and 3
steps backward, followed again by 5 steps forward and 3 steps
backward, and so on. Each step is 1 m long and requires 1 s. Plot
the *x*-*t* graph of his motion. Determine graphically
and otherwise how long the drunkard takes to fall in a pit 13 m
away from the start.

**Answer :**

Q5 :
**
**

A jet airplane travelling at the speed of 500 km
h^{-1} ejects its products of
combustion at the speed of 1500 km
h^{-1} relative to the jet plane.
What is the speed of the latter with respect to an observer on
ground?

**Answer :**

Q6 :
**
**

A jet airplane travelling at the speed of 500 km
h^{-1} ejects its products of
combustion at the speed of 1500 km
h^{-1} relative to the jet plane.
What is the speed of the latter with respect to an observer on
ground?

**Answer :**

Q7 :
**
**

Two trains A and B of length 400 m each are moving on two
parallel tracks with a uniform speed of 72 km
h^{-1} in the same direction, with A
ahead of B. The driver of B decides to overtake A and accelerates
by 1 m/s^{2}. If after 50 s, the guard of B just brushes
past the driver of A, what was the original distance between
them?

**Answer :**

Q8 :
**
**

On a two-lane road, car A is travelling with a speed of 36 km
h^{-1}. Two cars B and C approach car
A in opposite directions with a speed of 54 km
h^{-1} each. At a certain instant,
when the distance AB is equal to AC, both being 1 km, B decides
to overtake A before C does. What minimum acceleration of car B
is required to avoid an accident?

**Answer :**

Q9 :
**
**

Two towns A and B are connected by a regular bus service with a
bus leaving in either direction every *T* minutes. A man
cycling with a speed of 20 km h^{-1}
in the direction A to B notices that a bus goes past him every 18
min in the direction of his motion, and every 6 min in the
opposite direction. What is the period *T* of the bus
service and with what speed (assumed constant) do the buses ply
on the road?

**Answer :**

Q10 :
**
**

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).

**Answer :**

Q11 :
**
**

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 mustbe speeding up.

**Answer :**

Q12 :
**
**

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.

**Answer :**

Q13 :
**
**

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].

**Answer :**

Q14 :
**
**

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!]

**Answer :**

Q15 :
**
**

In Exercises 3.13 and 3.14, 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?

**Answer :**

Q16 :
**
**

Look at the graphs (a) to (d) (Fig. 3.20) carefully and state,
with reasons, which of these *cannot* possibly represent
one-dimensional motion of a particle.

**(a)**

**(b)**

**(c)**

**(d)**

**Answer :**

Q17 :
**
**

Figure 3.21 shows 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.

(Fig 3.21)

**Answer :**

Q18 :
**
**

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).

**Answer :**

Q19 :
**
**

Suggest a suitable physical situation for each of the following graphs (Fig 3.22):

**(a)**

**(b)**

**(c)**

(Fig: 3.22)

**Answer :**

Q20 :
**
**

Figure 3.23 gives the *x-t* plot of a particle executing
one-dimensional simple harmonic motion. (You will learn about
this motion in more detail in Chapter14). Give the signs of
position, velocity and acceleration variables of the particle at
*t* = 0.3 s, 1.2 s, - 1.2 s.

**(Fig: 3.23)**

**Answer :**

Q21 :
**
**

Figure 3.24 gives the *x-t* plot of a particle in
one-dimensional motion. Three different equal intervals of time
are shown. In which interval is the average speed greatest, and
in which is it the least? Give the sign of average velocity for
each interval.

(Fig: 3.24)

**Answer :**

Q22 :
**
**

Figure 3.25 gives a speed-time graph of a particle in motion
along a constant direction. Three equal intervals of time are
shown. In which interval is the average acceleration greatest in
magnitude? In which interval is the average speed greatest?
Choosing the positive direction as the constant direction of
motion, give the signs of *v* and *a* in the three
intervals. What are the accelerations at the points A, B, C and
D?

(Fig: 3.25)

**Answer :**

Q23 :
**
**

A three-wheeler starts from rest, accelerates uniformly with 1 m
s^{-2} on a straight road for 10 s,
and then moves with uniform velocity. Plot the distance covered
by the vehicle during the n^{th} second (n =
1,2,3….) versus n.
What do you expect this plot to be during accelerated motion: a
straight line or a parabola?

**Answer :**

Q24 :
**
**

A boy standing on a stationary lift (open from above) throws a ball upwards with the maximum initial speed he can, equal to 49 m/s. How much time does the ball take to return to his hands? If the lift starts moving up with a uniform speed of 5 m/s and the boy again throws the ball up with the maximum speed he can, how long does the ball take to return to his hands?

**Answer :**

Q25 :
**
**

On a long horizontally moving belt (Fig. 3.26), a child runs to
and fro with a speed 9 km h^{-1} (with
respect to the belt) between his father and mother located 50 m
apart on the moving belt. The belt moves with a speed of 4 km
h^{-1}. For an observer on a
stationary platform outside, what is the

(a) speed of the child running in the direction of motion of the belt ?.

(b) speed of the child running opposite to the direction of motion of the belt ?

(c) time taken by the child in (a) and (b) ?

Which of the answers alter if motion is viewed by one of the parents?

(Fig: 3.26)

**Answer :**

Q26 :
**
**

Two stones are thrown up simultaneously from the edge of a cliff
200 m high with initial speeds of 15 m/s and 30 m/s. Verify that
the graph shown in Fig. 3.27 correctly represents the time
variation of the relative position of the second stone with
respect to the first. Neglect air resistance and assume that the
stones do not rebound after hitting the ground. Take *g* =
10 m/s^{2}. Give the equations for the linear and curved
parts of the plot.

**Answer :**

Q27 :
**
**

The speed-time graph of a particle moving along a fixed direction
is shown in Fig. 3.28. Obtain the distance traversed by the
particle between (a) *t* = 0 s to 10 s, (b) *t* = 2 s
to 6 s.

(Fig. 3.28)

What is the average speed of the particle over the intervals in (a) and (b)?

**Answer :**

Q28 :
**
**

The velocity-time graph of a particle in one-dimensional motion is shown in Fig. 3.29:

Which of the following formulae are correct for describing the
motion of the particle over the time-interval
*t*_{2} to *t*_{1}?

(a) *x*(*t*_{2}) *=
x*(*t*_{1}) *+
v*(*t*_{1})(*t*_{2}*â€“t*_{1})
*+* ()*a*(*t*_{2}*â€“t*_{1})^{2}

(b) *v*(*t*_{2})*=
v*(*t*_{1}) *+
a*(*t*_{2}*â€“t*_{1})

(c) *v*_{Average} *=*
(*x*(*t*_{2}) *â€“
x*(*t*_{1})) */* (*t*_{2}
*â€“ t*_{1})

(d) *a*_{Average} *=*
(*v*(*t*_{2}) *â€“
v*(*t*_{1})) */* (*t*_{2}
*â€“ t*_{1})

(e) *x*(*t*_{2}) *=
x*(*t*_{1}) *+*
*v*_{Average}(t_{2}
*â€“* t_{1}) *+* ()*a*_{Average}(t_{2}
*â€“* t_{1})^{2}

(f) *x*(*t*_{2}) *â€“
x*(*t*_{1}) *=* area under the
*vâ€“t* curve bounded by the *t*-axis
and the dotted line shown.

**Answer :**

Physics Part-1 - Physics : CBSE ** NCERT ** Exercise Solutions for Class 11th for ** Motion In A Straight Line ** will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

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