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Speed is the physical quantity that is obtained from distance travelled and time taken. Speed is defined as the distance travelled per unit time.

The correct answer c) 0.216 km/h

The correct answer b) uniform acceleration

The correct answer b) the direction of car varies continuously

Speed gives an idea of how slow or fast a body is moving

Acceleration is the rate of change of velocity a = \(\frac{Δv}{Δt}\)

The SI unit of acceleration is m/sec²

If the rate of change of velocity is negative, then it is called deceleration (Retardation) denoted by ‘-a’.

(i) Retardation is the term used for negative acceleration. 

Explanation: If the velocity of an object is decreasing, it is said to have negative acceleration. 

(ii) A bus starting from rest attains a velocity of 54 km/h in 60 s, its acceleration is 0.25 m/s² . 

Explanation: initial velocity = 0 

time = 60 secs 

final velocity = 54 km/hr =\(\frac{54\,\times\,1000}{60\,\times\,60}\) m/s = 15 m/s 

Acceleration = \(\frac{change\,in\,velocity}{time\,taken}\)

= \(\frac{final\,velocity\,(v)\,-intial\,velocity(u)}{time\,taken(t)}\) 

= \(\frac{15\frac{m}{s}-0}{60 sec}\)= = 0.25 m/s²

(i) Acceleration depends on the change in the velocity and the time taken by the object to travel. 

(ii) Acceleration = \(\frac{change\,in\,velocity}{time\,taken}\)

= \(\frac{final\,velocity\,(v)-\,initial\,velocity(u)}{time\,taken(t)}\)

SI unit of acceleration is meter per second square (m/s²).

A graph represents the relation between two variable quantities in pictorial form. It is plotted between two variable quantities. The quantity that is varied our choice is called independent variable. The other quantity, which varies as a result of this change, is called dependent variable. For example, in distance-time graph, time is independent variable and distance is dependent variable. Similarly, in velocity-time graph, time is independent variable and velocity is dependent variable.

a) Velocity is defined as the distance travelled by the body in unit time in a given direction. The SI unit of velocity is m/s.

b) The difference between speed and velocity is: 

i) Speed is a scalar quantity while velocity is a vector quantity. 

ii) Speed is always positive while velocity can be either positive or negative. 

iii) Speed is defined as the distance travelled in unit time while velocity is the distance travelled in unit time in a particular direction. 

c) Speed = 54 km/h = (54)(1000/3600) = 15 m/s

Total distance = 200 km 

Average speed = 70 km/h 

Total time taken = total distance/average speed = 200/70 = 20/7 h 

First part of the journey, 

Distance = 100 km 

Speed = 50 km/h 

Time taken, t₁ = 100/50 = 2h 

Second part of the journey, 

Distance = 100 km Speed = x km/h 

Time taken, t₂ = 100/x h 

t₁ + t₂ = 20/7 

x = 116.6 km/h

Two uses of Graphical representation of motion are:

• Just by looking at the shape of the curve we can tell the nature of motion (i.e. uniform motion, non uniform, uniformly accelerated etc.) 

For Example, 

• if the distance – time graph is having straight line passing through origin then we can say that the motion is uniform motion. 
• if the graph line is not straight, then it is non uniform motion. 
• We can deduce different quantities and also derive equation of motion from graphs. 

For example, 

• from the distance – time graph, if we calculate the slope of the graph line, then we can ind the velocity of the object. 
• Also from the velocity – time graph, if we ind the slope of the graph then we can ind the acceleration of the object.

Average speed of a body is defined as the total distance travelled divided by the total time taken to cover the distance.

Average speed = \(\frac{total\,distance\,travelled}{total\,time\,taken}\)

Let us consider a car is travelling 2 Km in 30 minutes and then next 3 Km at 20 minutes. Then the average speed of the car is 

Average speed =\(\frac{5}{30+20}\) = 0.1 Km/min

No, earth moves round the sun with uniform speed, but its velocity changes continuously

Initial velocity, u = 5 m/s 

Final velocity, v = ? 

Acceleration, a = 0.2 m/s² 

Time, t = 10 s 

v = u + at = 7 m/s

Random motion : 

The motion that changes its direction and speed continuously is called random motion, 

e.g. Motion of a butterfly

Oscillatory motion :

The motion of a body that is swinging back and forth is called oscillatory motion, 

e.g. Pendulum of a clock, the wing of a bird.

Linear motion : 

Motion in a straight line is called linear motion.

e.g. Motion of a train.

Random motion :

The motion that changes its direction and speed continuously is called random motion, 

e.g. Motion of a bird.

1. Linear motion:

• Rolling of ball on ground 
• Moving of bicycler on road

2. Spinning motion :

• Rotating fan 
• Wheel of sewing machine

3. Oscillatory motion: 

• Pendulum of clock
• Motion of a child on a swing

4. Periodic motion:

• Pendulum of clock 
• Motion of a heart beat

5. Vibrational motion: 

• String of a guitar 
• Surface of drums

6. Circular motion:

• Rotation of a fan 
• Bicycle of whee

7. Random motion: 

• Motion of foot ball player 
• Movement of mosquito

The following results can be deduced from velocity-time graph.

• The acceleration produced in a body

• The distance covered by a moving object

• We can derive the equations of motion

Suppose an athlete takes t seconds to go once around the circular path of radius r, then the velocity v is given by the relation

v = distance travelled / time

Distance travelled = circumference of the circle

= 2r

Linear velocity = 2πr/t

The variable quantities in a uniformly accelerated rectilinear motion are time, speed, distance covered and acceleration. Simple relations exist between these quantities. These relations are expressed in terms of equations called equations of motion

The equations of motion are:

(1) v = u + at

(2) S = ut + ½ at²

(3) v² - u² = 2aS

Correct option is B) B

Correct option is B) m/s

Correct option is B) Newton

Correct option is A) v = u + at

C) v² – u² = 2as 

 A) a = \(\cfrac{v-u}t\)

Correct option is C) 4

Correct option is D) A and C

The rate of change of velocity in an object is known as its acceleration.

Distance is the length of the path traversed by an object in a given time interval and displacement is the shortest distance covered by the object in a specific direction.

1. Circular motion

2. Linear motion 

3. Circular motion 

4. Linear motion 

5. Oscillatory motion 

6. Oscillatory motion 

7. Circular motion 

8. Circular motion 

9. Bird – Random; Wings – Oscillatory motion 

10. Circular motion 

11. Linear, circular

No, we move in random motion.

Option : (d) random

Option : (c) speed

(1) Uniform linear motion :

When the distance traversed by an object along a straight line in unit time is the same, the motion is called as uniform linear motion, 

e.g. Motion of soldiers on parade.

(2) Non-uniform linear motion :

When the distance traversed by an object along a straight line in unit time keeps on changing, the motion is called non-uniform linear motion. 

e.g. A girl coming down a slide.

(3) Non-linear motion :

The motion of an object that does not move in a straight line is called non-linear motion. 

e.g. Motion of a swing,

(4) Speed :

The distance traversed by an object in unit time is called the speed of that object. 

e.g. A boy riding on a bicycle covers a distance of 15 kilometres in 3 hours.

Hence,

Speed = \(\frac{15}{3}\) 

= 5 kilometres/hour