# Motion : NCERT Exercise Question Q.1 An athlete completes one round of a circular track of diameter 200 m in 40s. What will be the distance and displacement at the end of 2 minutes 20 s ?

(i) Distance covered in 40 s

$= 2 \times \pi \times 100$

$\left( {r = {d \over 2} = {{200\,m} \over 2} = 100m} \right)$

Distance covered in 1 s

$= {{200\,\pi } \over {40}}$

Distance covered in 2 min 20s or 140 s

$= {{200\pi } \over {40}} \times 140$

$= 5\pi \times 140$

$= 700\pi$

$= 700 \times 3.14$

$= 2198{\mkern 1mu} m$

(ii) Displacement in 2 min 20 s = 0 m (initial and final position is the same).

Q.2 Joseph jogs from one end A to the other end B of a straight 300 m road in 2 minutes 50 seconds and then turns around and jogs 100 m back to point C in another 1 minute. What are joseph’s average speeds and velocities in jogging

(a) from A to B and

(b) from A to C ?

(a) From A to B

Distance = 300 m

Time = 2 min 50 s = 170 s

verage speed = Total distance / Total time

$= {{300m} \over {170s}} = 1.76\,m{s^{ - 1}}$

Average velocity = Displacement / Total time

$= {{300m} \over {170s}} = 1.76\,m{s^{ - 1}}$

(b) From A to C

Distance = (300 + 100)m = 400 m

Time = (170 + 60)s = 230 s

Average speed = Total distance / Total time

$= {{400m} \over {230s}} = 1.73\,m{s^{ - 1}}$

Average velocity = Displacement / Total time

$= {{200m} \over {230s}}$

$= 0.86m{s^{ - 1}}$

Q.3 Abdul, while driving to school computes the average speed for his trip to be 20 km h–1. On his return trip along the same route, there is less traffic and the average speed is 40 kmh –1. What is the average speed for Abdul’s trip ?

Let the distance between starting point and school be x km.

Average speed from the starting point to school

= 20 km h–1

Time for onward journey $= {x \over {20}}h$

Average speed from the school to the starting point

= 40 km h–1

Time for return journey $= {x \over {40}}h$

Average speed for total trip

= Total distance / Total time

$= {{2x} \over {{x \over {20}} + {x \over {40}}}}$

${{2x} \over {{{21x} \over {40}}}}$

$= 2x \times {{40} \over {21x}} = {{80} \over {21}} = 3.8km/h$

Q.4 A motor boat starting form rest on a lake accelerates in a straight line at a constant rate of 3.0 m s–2 for 8.0 s. How far does the boat travel during this time ?

u = 0

A = 3ms–2

T = 8s

According to second equation of motion,

$s = ut + {1 \over 2}a{t^2}$

$s = 0 \times 8 + {1 \over 2} \times 3 \times {\left( 8 \right)^2}$

$s = 96m$

Q.5 A ball is gently dropped from a height of 20 m. If its velocity increases uniformly at the rate of 10  s–2, with what velocity will it strike the ground ? After what time will it strike the ground
s = 20 m

u = 0

a = 10 ms-2 (since velocity increases at a uniform rate)

By second equation of motion

$s = ut + {1 \over 2}a{t^2}$

$s = 0 + {1 \over 2} \times 10 \times {t^2}$

$\Rightarrow 20 = 5{t^2}$

$\Rightarrow {{20} \over 5} = {t^2}$

$ort = \sqrt 4 = 2s$

By first equation of motion,

v = u + at

$\Rightarrow$ v = 0 + 10 × 2

$\Rightarrow$ v = 20 ms–1

Q.6 How do movements in the living and nonliving objects differ ?

The movements in living organisms appear to take place on their own. Nonliving bodies need some outside agency to set them into motion. For example, to run a car we need the chemical energy of petrol / diesel.

Q.7 What is motion ? Give some examples of motion in daily life.

(i) A body is said to be in motion if it changes its position in relation to a reference (fixed) point.

(ii) Some examples of motion in daily life are :

• Cars moving on the roads.

• Aeroplanes flying in the air.

• Blades of a fan going round.

• Different parts of machines moving in different ways.

• Fishes swimming in water.

Q.8 What is meant by the term distance?

The actual of the path covered by the body irrespective of the direction is called the distance. Distance is a scalar quantity

Q.9 What is displacement ?

Change in the position of an object in a particular direction is called displacement. If the position of an object changes from x1 to x2, then the displacement is given by

d = (x2 – x1)

Displacement is the shortest distance (straight distance) between the initial position and the final position of a moving body.

Displacement is a vector quantity, and it is the distance travelled by a body in a particular direction.

Q.10 When do we say that the position of a body has changed?

If the distance, or direction, or both, of a body relative to a reference point changes, then we say that the position of the body has changed.

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