Motion

Distance = 160 km;
time = 4 h

$\text{Average Speed} = \dfrac{\text{Total distance travelled}}{\text{total time taken}} \\[1em] \text{Average Speed} = \dfrac{\text{160}}{\text{4}} = 40 \text{km h}^{-1}$

So, average speed of the car = 40 km h^-1.

Distance = 300 km;
Average speed = 60 km h^-1
time = ?

$\text{Average speed} = \dfrac{\text{Distance travelled}}{\text{time}} \\[1em] \text{60} = \dfrac{\text{300}}{\text{time}} \\[1em] \text{time} = \dfrac{\text{300}}{\text{60}} = 5 \text{hr}$

So, time taken = 5 hour.

Average speed = 10 m s^-1;
time = 20 min
1 min = 60 sec
20 min = 60 x 20 = 1200 sec
distance = ?

$\text{Average speed} = \dfrac{\text{distance}}{\text{time}} \\[1em] \text{10} = \dfrac{\text{distance}}{\text{1200}} \\[1em] \text{distance} = 1200 \times 10 = 12000 \text{m}$

So, distance covered = 12000 m or 12 km.

The motion of the boy is non-uniform.
total distance travelled = 30 m + 30 m = 60 m
total time taken = 1 min + 1.5 min = 2.5 min
1 min = 60 sec
2.5 min = 2.5 x 60 = 150 sec
Average speed = ?

$\text{Average Speed} = \dfrac{\text{Total distance travelled}}{\text{total time taken}} \\[1em] \text{Average Speed} = \dfrac{\text{60}}{\text{150}} = 0.4 \text{m s}^{-1}$

So, average speed of the boy = 0.4 m s^-1.

(i) total distance travelled = 1 km + 0.5 km + 0.3 km = 1.8 km
total time taken = 1 h + 1 h + 1 h = 3 h

$\text{Average Speed} = \dfrac{\text{Total distance travelled}}{\text{total time taken}} \\[1em] \text{Average Speed} = \dfrac{\text{1.8}}{\text{3}} = 0.6 \text{km h}^{-1}$

So, average speed of the cyclist = 0.6 km h^-1.

(ii) total distance travelled = 1 km + 0.5 km + 0.3 km = 1.8 km
1 km = 1000 m
1.8 km = 1.8 x 1000 = 1800 m

total time taken = 1 h + 1 h + 1 h = 3 h
1 h = 3600 sec
3 h = 3 x 3600 = 10800 sec

$\text{Average Speed} = \dfrac{\text{Total distance travelled}}{\text{total time taken}} \\[1em] \text{Average Speed} = \dfrac{\text{1800}}{\text{10800}} = 0.167 \text{m s}^{-1}$

So, average speed of the cyclist = 0.167 m s^-1.

(a) In first part of journey
speed = 30 km h^-1

time = 30 min
60 min = 1 h
30 min = $\dfrac{\text{1}}{\text{2}}$ h

$\text{Speed} = \dfrac{\text{distance}}{\text{time}} \\[1em] \text{30} = \dfrac{\text{distance}}{\dfrac{1}{2}} \\[1em] \text{distance} = 30 \times {\dfrac{1}{2}} = 15 \text{km}$

In second part of journey
speed = 40 km h^-1

time = 1 h

$\text{Speed} = \dfrac{\text{distance}}{\text{time}} \\[1em] \text{40} = \dfrac{\text{distance}}{\text{1}} \\[1em] \text{distance} = 40 \times 1 = 40 \text{km}$

So, total distance travelled = 15 km + 40 km = 55 km.

(b) time taken in first part of journey = 30 min

60 min = 1 h
30 min = $\dfrac{\text{1}}{\text{2}}$ h

time taken in second part of journey = 1 h

total time taken = 1 h + $\dfrac{\text{1}}{\text{2}}$ h = 1.5 h

So, total time taken = 1.5 h.

(c) $\text{Average Speed} = \dfrac{\text{Total distance travelled}}{\text{total time taken}} \\[1em] \text{Average Speed} = \dfrac{\text{55}}{\text{1.5}} = 36.67 \text{km h}^{-1}$

So, average speed of the car = 36.67 km h^-1.

(a) Mass of boy = 37 kg

So, Weight of boy in kgf = 37 kgf.

(b) 1 kgf = 10 N
37 kgf = 37 x 10 = 370 N

So, weight of boy in N = 370 N.

(a) Mass of boy = 30 kg on moon surface as mass remains constant. Mass of a body does not change with place.

(b) Weight of body of mass 6.0 kg on moon surface = 10 N

Weight of body of mass 30 kg on moon surface = $\dfrac{\text{10}}{\text{6.0}}$ x 30 = 50 N

So, weight of boy of 30 kg on moon surface = 50 N.

(a) False
Correct Statement — Two trains going in opposite directions with the same speed are at motion relative to each other.

(b) False
Correct Statement — A ball is thrown vertically upwards. Its motion is non-uniform throughout.

(c) True

(d) True

(e) False
Correct Statement — A ball thrown by a boy from a roof-top has curvilinear motion.

(f) False
Correct Statement — Mass has only magnitude.

(g) True

(h) False
Correct Statement — Weight varies from place to place but mass does not.

(a) at rest

(b) straight line

(c) 2 s

(d) 10

(e) average speed

(f) 36 kg

(g) spring balance

a body at rest

Reason — A book lying on a table will not change its position if it is not disturbed, so it is said to be at rest.

oscillatory

Reason — The motion of pendulum is to and fro motion which is called oscillatory motion.

rectilinear motion

Reason — As the car is moving on a straight road so it is in rectilinear motion.

linear

Reason — A ball falls down vertically i.e. in a straight line, so its motion is linear.

uniform

Reason — If a moving body travels equal distances in equal intervals of time, then the motion is said to be uniform.

24 km h^-1

Reason — Suppose the distance between school and house is D km.

In first part the boy goes to school by bus from home at speed (V₁) = 20 km h^-1.

time taken (t₁) = $\dfrac{\text{distance}}{\text{speed}}$ =$\dfrac{\text{D}}{\text{20}}$

In second part the boy returns from school to home through same route at speed(V₂) = 30 km h^-1.

time taken (t₂) = $\dfrac{\text{distance}}{\text{speed}}$ =$\dfrac{\text{D}}{\text{30}}$

Total distance = D + D = 2D km

Total time taken = $\dfrac{\text{D}}{\text{20}}$ + $\dfrac{\text{D}}{\text{30}}$ = $\dfrac{\text{5D}}{\text{60}}$

Average speed = $\dfrac{\text{total distance travelled}}{\text{total time taken}}$

$\text{Speed} = \dfrac{\text{distance}}{\text{time}} \\[1em] = \dfrac{2D}{\dfrac{5D}{60}} \\[1em] = 2 \times 12 \\[1em] = 24 \text{km h}^{-1}$

500 N

Reason — Weight = 50 x 10 = 500 N

A body is said to be at rest if it does not change its position with respect to its immediate surroundings.

A body is said to be in motion if it changes its position with respect to its immediate surroundings.

An object can be in motion relative to one set of objects while at rest relative to some other set of objects. Thus, rest and motion are relative terms.
Example — If a boy is sitting on a bench in a bus stop and he sees a moving bus, for him the bus is in motion but the trees near by will appear to him at rest.
But a boy who is sitting inside a bus, to him the trees and the boy outside sitting on the bench will appear to move in opposite direction. But the roof of the bus and driver will appear to him at rest.
From the above example it can be concluded that rest and motion are relative terms.

(a) in motion, in motion

(b) at rest, in motion

The five different types of motion are:

1. Translatory motion
2. Circular motion
3. Oscillatory motion
4. Vibratory motion
5. Rotatory motion

A body is said to have translatory motion if every point on the moving body moves through the same distance in the same interval of time.
Example — Motion of a box when pushed from one corner of a room to the other.

(i) The motion of a body in a straight line is called rectilinear or linear motion.
Example — A car moving on a straight road.

(ii) If the motion of a body is along a curved path, it is said to be a curvilinear motion.
Example — The motion of a cycle while taking a turn on the road.

A body is said to be in a rotatory motion if it moves about a fixed axis.
Examples — a spinning top, a merry-go-round.

The motion of a body along a circular path is called circular motion. Example — Motion of a satellite around the earth.

The to and fro motion of a body from its rest position is called the oscillatory motion.
Example — Motion of a pendulum of a wall clock. The bob of pendulum moves to side A from its rest position O, again comes back to position O and then moves to side B and then comes back to rest position O. This process is continuously repeated and this to and fro motion is called oscillatory motion.

The to and fro motion of a part of the body keeping its rest part fixed is called vibratory motion.
Example — Vibration of the membrane of tabla.

The motion of an object which takes path in no specific direction is called random motion.
Example — Motion of molecules of a gas.

(a) Rectilinear motion

(b) Rotatory motion

(c) Oscillatory motion and Periodic motion

(d) Non-periodic motion

(e) Circular motion

(f) Periodic motion, circular motion

(g) Rotatory motion

The two examples that show a body can have two or more types of motion (mixed motion) simultaneously are:

1. The Earth rotates about its axis (rotatory motion) and at the same time, it revolves around the sun in a curved path (curvilinear or circular motion) in a fixed time interval (periodic motion).

2. A ball rolling on the ground has rotatory and translatory motion as it moves on the ground.

(a) Periodic motion

(b) Translatory and rotatory motion

(c) Translatory and rotatory motion

(d) Translatory and oscillatory motion

The average speed is calculated by finding the ratio of the total distance travelled by the body to the total time taken in the journey.

Average speed = $\dfrac{\text{total distance travelled}}{\text{total time taken}}$

The weight of the body on earth is the force with which earth attracts the body. The S.I. unit of weight is newton (N).

1 kgf = 9.8 (nearly 10) N

Mass does not change by change of place.

The direction of weight is always directed vertically downwards.