MOTION Online Test 9th science Lesson 2 questions in English

Motion is the change in the position of an object with respect to its surrounding. Everything in the universe is in motion. Even though an object seems to be not moving, actually it is moving because the Earth is moving around the Sun.

Motion is described in terms of distance, speed, acceleration and time.

In physics the objects which do not change their position are said to be at rest, while those which change their position are said to be in motion.

Motion is a relative phenomenon. This means that an object appearing to be in motion to one person can appear to be at rest as viewed by another person. For example, trees on road side would appear to move backward for a person travelling in a car while the same tree would appear to be at rest for a person standing on the road side.

Linear motion: Motion along a straight line.
Circular motion: Motion along a circular path.
Oscillatory motion: Repetitive to and fro motion of an object at regular interval of time.

Random motion: Motion of the object which does not fall in any of the categories is called as random motion. It is a type of motion that is unpredictable. In this type of motion the object moves in any direction, and the direction continually changes.

Consider a car which covers 60 km in the first hour, 60 km in the second hour, and another 60 km in the third hour and so on. The car covers equal distance at equal interval of time. We can say that the motion of the car is uniform.

An object is said to be in uniform motion if it covers equal distances in equal intervals of time howsoever big or small these time intervals may be.

Non-uniform motion: Now, consider a bus starting from one stop. It proceeds slowly when it passes through crowded area of the road. Suppose, it manages to travel merely 100 m in 5 minutes due to heavy traffic and is able to travel about 2 km in 5 minutes when the road is clear. Hence, the motion of the bus is non-uniform i.e. it travels unequal distances in equal intervals of time.

An object is said to be in non-uniform motion if it covers unequal distances in equal intervals of time.

An object moving from the point A moves along the path given in the Figure and reaches the point B. The total length of the path travelled by the body from A to B is called distance travelled by the body. The length of the straight line AB is called displacement of the body.

An object moving from one point moves along the path given and reaches another point. The total length of the path travelled by the body from start to end point is called distance travelled by the object.

Distance: The actual length of the path travelled by a moving body irrespective of the direction is called the distance travelled by the body. It is measured in meter in SI system. It is a scalar quantity having magnitude only.

Displacement: It is defined as the change in position of a moving body in a particular direction. It is a vector quantity having both magnitude and direction. It is also measured in meter in SI system.

Speed is the quantity which shows how fast the body is moving but velocity is the quantity which shows the speed as well as the direction of the moving body.

Speed is the rate of change of distance or the distance travelled in unit time.

Speed = Distance travelled / Time taken
Distance is 70 miles, Speed is 30mph
Time = 70/30
Time = 70/30 = 2.33
2.33 x 60 = 140 minutes = 2 hours and 20 minutes

Speed is a scalar quantity. The SI unit of speed is ms-1.

Total distance travelled by the object = 50 m + 30 m + 20 m = 100 m
Total time taken = 30s + 20s + 15s = 65 s
Average speed = Total distance travelled / Total time taken
s = 1.54 ms-1
Therefore, the average speed of the object is 1.54ms-1

Velocity is the rate of change of displacement. It is the displacement in unit time. It is a vector quantity.

The SI unit of velocity is ms-1.

Velocity = Displacement / Time taken

Acceleration is the rate of change of velocity or it is the change of velocity in unit time. It is a vector quantity. The SI unit of acceleration is ms-2.

Acceleration = Change in velocity/Time = (Final velocity – Initial velocity)/Time
a = (v–u)/t

Consider a situation in which a body moves in a straight line without reversing its direction. From the above equation if v > u, i.e. if final velocity is greater than initial velocity, the velocity increases with time and the value of acceleration is positive.

If v < u, i.e. if final velocity is less than initial velocity, the velocity decreases with time and the value of acceleration is negative. It is called negative acceleration.

Negative acceleration is called retardation or deceleration. If the acceleration has a value of –2 ms-2, we say that deceleration is 2 ms-2.

In the distance – time graph for a Uniform motion it is a straight line. It shows that the speed is constant. The parameter speed is referred as the slope of the line. Speed = Distance covered / Time taken = Slope of the straight line = BC/AC. Steeper the slope (in other words the larger value) the greater is the speed.

The slope of the line on the distance – time graph becomes steeper and steeper as the speed increases.

This Distance-time graph shows non–linear variation of the distance travelled by the object with time. Thus, the graph represents motion with non-uniform speed for a Non-uniform motion.

The variation in velocity of an object with time can be represented by velocity – time graph. In the graph, time is represented along the X – axis and the velocity is represented along the Y – axis. If the object moves at uniform velocity, a straight line parallel to X-axis is obtained.

The area under the velocity – time graph is equal to the magnitude of the displacement. So, the distance (displacement), S covered by the object in a time interval of t can be expressed as,

S = AC × CD

S = Area of the rectangle ABCD (shaded portion in the graph)

The nature of the graph shows that the velocity changes by equal amounts in equal intervals of time. Thus, for all uniformly accelerated motion, the velocity – time graph is a straight line.

The magnitude of the velocity of the object is changing due to acceleration. The distance, S travelled by the object will be given by the area under the velocity – time graph.

In the case of non-uniformly accelerated motion, distance – time graph and velocity – time graphs can have any shape.

The speedometer of an automobile measures the instantaneous speed of the automobile.

In a uniform motion in one dimension, the average velocity is equal to instantaneous velocity. Instantaneous velocity is also called velocity or instantaneous speed or simply speed.

Newton studied the motion of an object and gave a set of three equations. These equations relate displacement, velocity, acceleration and time of an object under motion.

An object in motion with initial velocity, u attains a final velocity, v in time, t due to acceleration a and reaches a distance s. Three equations can be written for this motion.

v = u + at

s = ut + ½ a t2

v2 = u2 + 2as

First equation of motion: By definition, Acceleration = Change in velocity / Time  = (Final velocity – Initial velocity)/Time

v = u + at This is the first equation of motion.

Initially trolley at rest position so u = 0, Given a = 2 m /s² and t = 3s

From Newton’s first law of motion v = u + at

v = 6 m/ s

Second equation of motion s = u t + ½ at²

The distance covered by the object during time, t is given by the area of the trapezium.

Then, s = Area of trapezium

= ½ × Sum of length of parallel side × Distance between parallel sides

s = ½ × (u + v) × t

Since, a= (v – u) / t or t = (v – u)/a

s = ½ × (v + u) × (v – u)/a

2as = v²   – u ²

v² = u² + 2 as

The equation of motion for a freely falling body can be obtained by replacing ‘a’ in equations with g, the acceleration due to gravity. For a freely falling body which is initially at rest, u = 0. Thus we get the following equations. v = gt, s = ½ gt², v² = 2gh

When a body is thrown vertically upwards in space, at the highest point, the body has zero velocity but it has acceleration due to the gravity.

When we throw an object vertically upwards, it moves against the acceleration due to gravity. Hence, ‘a’ is taken to be –g and when moving downwards ‘a’ is taken as +g.

Uniform circular motion is a specific type of motion in which an object travels in a circle with a constant speed. For example, any point on a propeller spinning at a constant rate is executing uniform circular motion. The velocity vector is tangent to the trajectory at each point and its direction is the same as the direction of the motion. This means that the motion has normal acceleration. In non-uniform circular motion an object is moving in a circular path with a varying speed. Since the speed is changing, there is tangential acceleration in addition to normal acceleration.

When an object is moving with a constant speed along a circular path, the velocity changes due to the change in direction. Hence, it is an accelerated motion.

For example, revolution of earth around the sun, revolution of moon around the earth and the tip of the second’s hand of a clock are all accelerated motions.

If an object, moving along a circular path of radius, r takes time, T to come back to its starting position then the speed V is given by, Speed = Circumference/Time taken; V = 2 π r/T

A body is said to be accelerated, if the velocity of the body changes either in magnitude or in direction. So, the motion of a stone in circular path with constant speed and continuous change of direction is an accelerated motion.

In the case of an object tied to string moving in a circular path with const speed and continuous change of direction there must be an acceleration acting along the string directed inwards, which makes the stone to move in circular path. This acceleration is known as centripetal acceleration and the force is known as centripetal force. Since the centripetal acceleration is directed radially towards the center of the circle the centripetal force must act on the object radially towards the center.

Let us consider an object of mass m, moving along a circular path of radius r, with a velocity, v. Its centripetal acceleration is given by a = v2 /r

The magnitude of centripetal force is given by, F = Mass × Centripetal acceleration

F = mv 2 / r

Net force acting upon an object, F = m a ;  m = F / a ; m  = 250 / 5 = 50

Any force like gravitational force, frictional force, magnetic force, electrostatic force may act as a centripetal force.

A pulling force that acts away from the center is called as centrifugal force. Force acting on a body away from the center of circular path is called centrifugal force. Thus, centrifugal force acts in a direction which is opposite to the direction of centripetal force.

Its magnitude is same as that of centripetal force. The dryer in a washing machine is an example for the application of centrifugal force.

For an accelerated motion, the distance-time graph is not a straight line. For a uniform acceleration, the graph is a parabola. The figure b) shows the graph for a uniformly accelerated motion. For non-uniform acceleration, the graph has irregular shape.

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