Motion

IMPORTANT TERMS

Motion

Change of position is called motion. It can be best described in terms of distance moved or displacement. Change in position is taken with respect to an object at rest which is called reference point.

Uniform Motion: Body covers equal distance in equal time interval.

Non-Uniform Motion: Body covers unequal distance in equal time interval.

Speed

Distance travelled per unit time is called speed. SI unit for speed is m/s.

Speed = Distance travelled/Time taken

It is a scalar quantity as it has magnitude only.

Average Speed: The ratio of total distance travelled to the total time taken by the body      gives its average speed.

A body is said to have constant or uniform speed if it travels equal distance in equal interval of time.

Velocity

Displacement per unit time is known as velocity. It is nothing but speed of an object in a definite direction.

Velocity = Displacement/Time taken

It is a vector quantity as it has both magnitude and direction.

Average Velocity: It is the arithmetic mean of initial velocity and final velocity for a given       period of time.

Acceleration

Rate of change of velocity with time is known as acceleration. SI unit of acceleration is     m/s^2.

Acceleration = Change in velocity/Time taken

A body has uniform acceleration if it travels in a straight line and its velocity increases by equal amounts in equal intervals of time.

A body has non uniform acceleration if it travels in a straight line and its velocity increases or decreases by unequal amounts in equal intervals of time.

Distance

Actual length of path covered by a moving body is called distance. Distance is independent of direction, hence it is a scalar quantity.

Displacement

When a body moves from one position to another the shortest distance between the initial and final position of the body along with its direction is known as displacement. It is a vector quantity.

EQUATIONS OF MOTION

First Equation of Motion: Velocity - time relationship

The first equation of motion is v = u + at, where v is the final velocity and u is the initial velocity of the body and a is uniform acceleration.

First equation of motion gives velocity acquired by body at any time t.

Second Equation of Motion: Position - time relationship

Second equation of motion is s = ut + 1/2 at^2, where u is initial velocity, a is uniform acceleration and s is the distance travelled by body in time t.

Second equation of motion gives distance travelled by a moving body in time t

Third Equation of Motion: Position - Velocity relationship

Third equation of motion is v^2 = u^2 + 2as, where u is initial velocity, v is the final velocity, a is uniform acceleration and s is the distance travelled by the body.

This equation gives the velocity acquired by the body in travelling a distance s.

GRAPHICAL REPRESENTATION OF MOTION

To describe motion of an object, we can use line graphs.

Distance Time Graphs

Slope of distance time graph can be used to calculate speed of a body.

Distance on y axis, time on x axis.

Interpretation:

For uniform speed: Straight line.

For non-uniform speed: Curved line.

For Increasing speed: Straight line sloping upwards.

For decreasing speed: Straight line sloping downwards.

For objects at rest: Straight line parallel to x axis.

Velocity Time Graphs

Slope of velocity time graph can be used to calculate acceleration.

Area enclosed by velocity time graph and time axis gives magnitude of displacement.

Velocity on y axis, time on x axis.

Interpretation:

Velocity time graph when speed remains constant (no acceleration): Straight line parallel to x axis.

Velocity time graph showing acceleration: Straight line.

UNIFORM CIRCULAR MOTION

When an object moves in a circular path at a constant speed then motion of the object is called uniform circular motion.

Examples of uniform circular motion are:

(a) Motion of artificial satellites around the earth.

(b) Moon moves in uniform circular motion round the earth.

(c) Cyclist moving on a circular track with a constant speed

IMPORTANT POINTS TO REMEMBER

• Simplest case of motion is rectilinear motion which is the motion of the object in a   straight line
• Displacement can be zero when distance is not zero
• Speed, Distance, Time are scalar quantities and Velocity, Acceleration, Displacement are vector quantities.
• Acceleration is zero when a body moves with uniform velocity.
• If acceleration is in the direction of the velocity then it is positive acceleration and if it is in the direction opposite to the direction of velocity then it is negative and the negative acceleration is termed retardation or deceleration.

INTERESTING FACTS

• Everything in this world is moving. Even things that seem still are in motion, because the atoms inside them are vibrating.
• When an object moves in a circle, the force that constantly pulls it towards the centre and stops it from flying off in a straight line is called centripetal force.
• Two cars driving at the same speed have different velocities if one of them goes north and the other goes south.
• In space there is nothing for the rocket to push on. Therefore, the rocket is propelled by the action and reaction between the hot gases pushed out by its engine and the rocket itself.
• When a ball is bounced on the ground, it is not only the ball that recoils but the Earth too. The Earth’s mass is so much compared to the ball’s, that the recoil is insignificant to show.
• It is said that Isaac Newton got the idea for gravity when an apple fell off a tree and hit him on the head.