MOTION

 MOTION

DISTANCE & DISPLACEMENT

Distance: Distance is the length of the path (the line or curve) described by an object moving through space. Distance is independent of direction. Thus, such physical quantities that do not require direction for their complete description are called scalars.

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. Displacement has both direction and magnitude for its complete description and hence such physical quantities are called a vector.

NOTE: The distance travelled by a moving body cannot be zero but the final displacement of a moving body can be zero.

UNIFORM & NON-UNIFORM MOTION

Uniform Motion: If a body covers equal distances in equal intervals of time, then it is said to be having uniform motion.

Non-Uniform Motion: If a body covers unequal distances in equal intervals or equal distances in unequal intervals then body is said to be having non-uniform motion.

SPEED

Speed is defined as the total distance travelled by the object in the time interval during which the motion takes place. SI unit of speed is meter per second.

where s is the distance travelled by the body and t is the time taken by the body to travel distance s.

 

 

VELOCITY

The rate of change of displacement of a body with the passage of time is known as velocity of the body. Velocity of an object is measured in meter per second in SI units.

• Velocity is nothing but the speed of an object moving in a definite direction.
• The velocity of an object can be uniform or variable. It can be changed by changing the object’s speed, direction of motion or both.
• So velocity of a body is a vector quantity involving both distance and displacement whereas speed of a body is a scalar quantity and it only has magnitude and does not have specific direction.
• Thus a body is said to be moving with uniform velocity if it covers equal distances in equal intervals of time in a specified direction.
• A body is said to be moving with non-uniform velocity if it covers unequal distances in equal intervals of time and vice-versa in a specified direction or if it changes the direction of motion.

ACCELERATION

Acceleration is a measure of the change in the velocity of an object per unit time and mathematically it is given as

If the velocity of an object changes from an initial value u to the final value v in time t, the acceleration a is given by,
a=(v−u)/t

• A body has uniform acceleration if it travels in a straight line and its velocity increases by equal amount in equal intervals of time for example freely falling bodies, motion of ball rolling down the inclined plane etc.
• A body has non uniform acceleration if its velocity increases or decreases by unequal amount in equal intervals of time.
• 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.
• SI unit of acceleration is ms^-2.

EQUATIONS OF MOTION

There are three equations of bodies moving with uniform acceleration which we can use to solve problems of motion

1.       First Equation of motion v=u+at

2.       Second Equation of motion s=ut+1/2at² 

3.       Third equation of motion v²=u²+2as

 

Graphical representation of motion

Distance Time Graphs

 

Velocity time graphs

 

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.
• In our everyday life, we came across many examples of circular motion for example cars going round the circular track and many more. Also earth and other planets revolve around the sun in a roughly circular orbit
• If the speed of motion is constant for a particle moving in a circular motion still the particles accelerate because of constantly changing direction of the velocity.
• If an object moves in a circular path with uniform speed, its motion is called uniform circular motion.
• In circular motion, we use angular velocity in place of velocity we used while studying linear motion.
• Force which is needed to make body travel in a circular path is called centripetal force. 

• We know that the circumference of a circle of radius ‘r’ is given by ‘2πr’. If the body takes t seconds to go once around the circular path of radius ‘r’, the velocity ‘v’ is given by v=2πrt.
• Uniform linear motion is not accelerated but uniform circular motion is accelerated motion.
• Examples of uniform circular motion are

(a) Motion of artificial satellites around the earth

(b) Moon, the natural satellite of earth, moves in uniform circular motion round the earth.

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