## Short Questions

#### 2.2 Explain translator motion and give examples of various types of translator motion.

Ans: Translatory motion:

In translation motion, a body moves along a line without any rotation. The line may be straight or curved.

Examples:

Riders moving in Ferris wheel are also in translational motion. Their motion is in a circle without rotation.

Types of Translatory motion:

Translatory motion can be divided into linear motion, circular motion and random motion.

1. Linear motion:

Straight-line motion of a body is called linear motion.

Examples:

The motion of objects such as a car moving on a straight and level road is linear motion.

Aeroplanes flying straight in air and objects falling vertically down are also the examples of linear motion.

1. Circular motion:

The motion of an object in a circular path is called circular motion.

Examples:

A stone tied at the end of a string can be made to whirl. The stone moves in a circle and thus has circular motion.

Toy train moving on a circular track. A bicycle or a car moving along a circular track possess circular motion.

The motion of the earth around the sun and motion of the moon around the earth are also examples of circular motion.

• Random Motion:

The disordered or irregular motion of an object is called random motion.

Examples:

The motion of insects and birds are irregular. Thus, the motion of insects and birds is a random motion.

The motion of dust or smoke particles in the air is also random motion.

The Brownian motion of a gas or liquid molecules along a zigzag path such as shown in the figure is also an example of random motion.

#### (vi) Scalers and Vectors

Ans:

• Difference between Rest and motion:

Rest:

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

Motion:

A body is said to be at rest, if it changes its position with respect to its surroundings.

The state of rest or motion of a body is relative. For example, a passenger sitting in a moving bus is at rest because he/she is not changing his/her position with respect to the other passengers or objects in the bus but to an observer outside the bus the passengers the objects inside the bus are in motion

• Difference between Circular and rotatory motion:

Circular motion:

Any turning as if on-axis is rotatory motion. Any rotatory motion where the radius of gyration, length and axis of rotation is fixed is circular motion. And that is the difference. Circular motion is just a special case of rotatory motion. That is, there is no fixed axis and radius restriction for rotatory motion. But there is for circular motion.

For example, all planets have rotatory motion around their suns but most of the orbits are elliptical. Therefore, rotation axis and radius of gyration vary as they trek around. So, most, if not all, planets do not have circular motion.

Note:

Gyration length:

A length that represents the distance in a rotating system between the point about which it is rotating and the point to and from which the transfer of energy has the maximum effect.

• Difference between distance and displacement:

 Distance Displacement Length of the path between two points is called the distance between those points. Displacement is the shortest distance between two points which has magnitude and direction Distance is a scalar quantity Displacement is a vector quantity Distance is denoted by “S”. S=vt Its unit is meters (m). Displacement is denoted by “d”. d=vt Its SI unit is meter (m). Distance(S) dotted lines, Displacement(d) dark lines from point A to B.

• Differentiate between speed and velocity

 Speed Velocity The distance covered by an object in unit time is called speed. Distance=speed x time Or S=vt The rate of displacement of a body is called velocity. V=d/t or d=vt Speed is a scalar quantity. Velocity is a vector quantity. SI unit of speed is SI unit of velocity is the same as the speed

(v)  Difference between linear and random motion

• Linear motion:

Straight-line motion of a body is called linear motion.

Examples:

The motion of objects such as a car moving on a straight and level road is linear motion.

Aeroplanes flying straight in air and objects falling vertically down are also the examples of linear motion.

• Random Motion:

The disordered or irregular motion of an object is called random motion.

Examples:

The motion of insects and birds are irregular. Thus, the motion of insects and birds is a random motion.

The motion of dust or smoke particles in the air is also random motion.

The Brownian motion of a gas or liquid molecules along a zigzag path such as shown in the figure is also an example of random motion.

(vi)  Difference between scalers and vectors:

 Scalers Vectors A scalar quantity is described completely by its magnitude only. A vector quantity is described by its magnitude and direction. Examples Examples of scaler are mass, length, time, speed, volume, work, energy, density, power, charge, pressure, area, temperature. Examples Examples of the vector are velocity, displacement, force, momentum, torque, weight, electrical potential etc.

#### 2.4 Define the terms Speed, velocity and acceleration

Ans:

Speed:

The distance covered by an object in unit time is called speed.

v=S/t

Velocity:

The rate of displacement of a body is called velocity.

V=d/t

Acceleration:

Acceleration is defined as the rate of change of velocity of a body

Unit of acceleration:

SI unit of acceleration is meter per second square.

#### 2.5 Can a body moving at a constant speed have acceleration?

Ans:

Yes, when a body is moving with constant speed, the body can have acceleration if its direction changes. For example, if the body is moving along a circle with constant speed, it will have acceleration due to the change of direction at every instant.

#### 2.6 How do riders in a Ferris wheel possess Translatory motion but not circular motion?

Ans:

Riders in a Ferris wheel possess Translatory motion because their motion is in a circle without rotation.

#### 2.7 Sketch a distance-time graph from the body starting from rest. How will you determine the speed of the body from this graph?

Ans:

Distance-time graph for a body starting at rest:

When a body starting from rest then the distance-time graph is a straight line. Its slope gives the speed of the object.

Speed of a body from the graph:

Consider two points A and B on the graph

Speed of the object=slope of line AB

= Distance EF/Time CD=2

=2m/s

The speed found from the graph is 2m/s

#### 2.8 What would be the shape of a speed-time graph of a body moving with variable speed?

Ans:

An object moving with variable speed:

When an object does not cover equal distances in equal intervals of time then its speed is not constant. In this case, the distance-time graph is not a straight line.

The slope of the curve at any point can be found from the slope of the tangent at that point. For example,

the slope of the tangent at P

=3m/s

Thus, the speed of the object at P is 3m/s.

The speed is higher at instants when the slope is greater, speed is zero at instants when the slope is horizontal.

#### (iv) Acceleration of motion

Ans:

All the above factors can be obtained from a speed-time graph.

#### 2.10 How can vectors quantities can be represented graphically?

Ans:

Symbolic Representation of a vector:

To differentiate a vector from a scalar quantity, we generally use bold letters to represents vectors quantities such as F, a, d or a bar or an arrow over the symbols.

Graphical Representation of a vector:

A straight line is drawn with an arrow head at one end. The length of a line, according to some suitable scale, represents the magnitude and the arrow head gives the direction of the vector.

#### 2.11 Why vector quantities cannot be added or subtracted like scaler quantities?

Ans:

The scaler quantities obey the rules of arithmetic and ordinary algebra because scaler quantities have no directions, so vectors obey special rules of vector algebra, therefore, vectors are added by head to tail rule (vector algebra)

#### 2.12 How are vector quantities important to us in our daily life?

Ans:

We use vectors in almost every activity of life. A vector is a quantity that has both direction and magnitude.

Examples of everyday activities that involve vectors include:

• Breathing (your diaphragm muscles exerts a force that has magnitude and direction)
• Walking (you walk at a velocity of around 7 km/h in the direction of the bathroom)
• Going to school (the bus has a length of about 300m and is headed towards your school)
• Lunch (the displacement from your classroom to the canteen is about 50m in the north direction.
• To describe a car’s velocity, you would have to state it as 80km/h south.

Vectors are important as they describe physical processes in the real world, and without understanding them, we cannot understand how real-world works. Imagine how difficult it would be for an air traffic controller if he did not understand vectors when directing planes speeds and direction.

#### 2.13 Derive equations of motion for uniformly accelerated rectilinear motion.

Ans:

See Q36, 37 and 38 from notes.

#### 2.14 Sketch a velocity-time graph for the motion of the body. From the graph explaining each step, calculate total distance covered by the body.

Ans:

Velocity time graph:

Calculation of distance moved by an object from a velocity-time graph:

The distance moved by an object can also be determined by using its velocity-time graph.

• If an object moves at constant velocity v for time t. The distance covered by the object is v x t. the distance can also be found by calculating the area under the velocity-time graph. This area is shaded and is equal to v x t.
• If the velocity of the object increases uniformly from 0 to v in time t. the magnitude of its average

Distance covered = average velocity x time= 1/2v x t

Now we calculate the area under the velocity-time graph, which is equal to the area of the triangle shaded in the figure. Its value is equal to ½ base x height= ½ v x t

Note:

The area between the velocity-time graph and the time axis is numerically equal to the distance covered by the object.