Rest: A body is said to be in a state of rest when its position does not change with respect to a reference point.
Motion: A body is said to be in a state of motion when its position changes continuously with reference to a point.
Motion can be of different types depending upon the type of path by which the object is going through.
(i) Circulatory motion/Circular motion – In a circular path.
(ii) Linear motion – In a straight line path.
(iii) Oscillatory/Vibratory motion – To and fro path with respect to origin.
Scalar quantity: It is the physical quantity having its own magnitude but no direction.
Example: distance, speed.
Vector quantity: It is the physical quantity that requires both magnitude and direction.
Example: displacement, velocity.
Difference between Distance and Displacement
Uniform Motion
When a body travels an equal distance in an equal interval of time, then the motion is said to be uniform motion.
Non-uniform Motion
In this type of motion, the body will travel unequal distances in equal intervals of time.
Two types of non-uniform-motion
(i) Accelerated Motion: When the velocity of a body increases with time.
(ii) De-accelerated Motion: When the velocity of a body decreases with time.
The measurement of distance traveled by a body per unit of time is called speed.
Change from km/hr to m/s = 1000m/(60×60)s = 5/18 m/s
It is the speed of a body in a given direction.
For non-uniform motion in a given line, average velocity will be calculated in the same way as done in average speed.
It can be positive (+ve), negative (-ve) or zero.
Acceleration is seen in non-uniform motion and it can be defined as the rate of change of velocity with time.
(i) s/t graph for uniform motion:
(ii) s/t graph for non-uniform motion:
(iii) s/t graph for a body at rest:
v = (s2 - s1)/(t2 - t1)
But, s2 - s1
∴ v = 0/(t2 - t1) or v=0
(i) v/t graph for uniform motion:
a = (v2 - v1)/(t2 - t1)
But, v2 - v1
∴ a = 0/(t2 - t1) or a = 0
(ii) v/t graph for uniformly accelerated motion:
In uniformly accelerated motion, there will be an equal increase in velocity in equal intervals of time throughout the motion of the body.
(iii) v/t graph for non-uniformly accelerated motion:
a2 ≠ a1
(iv) v/t graph for uniformly decelerated motion:
or, a1' = a2'
(v) v/t graph for non-uniformly decelerated motion:
a1' ≠ a2'
Note: The area enclosed between any two-time intervals is ‘t2 - t1’ in the v/t graph, which will represent the total displacement by that body.
Total distance travelled by body between t2 and t1, time intervals
= Area of ∆ABC + Area of rectangle ACDB
= ½ × (v2 – v1)×(t2 - t1) + v1× (t2 - t1)
First Equation: v = u + at
Final velocity = Initial velocity + Acceleration × Time
Graphical Derivation
Suppose a body has initial velocity ‘u’ (i.e., the velocity at time t = 0 sec.) at point ‘A’, and this velocity changes to ‘v’ at point ‘B’ in ‘t’ secs. i.e., final velocity will be ‘v’.
For such a body there will be an acceleration.
a = Change in velocity/Change in Time
⇒ a = (OB - OA)/(OC-0) = (v-u)/(t-0)
⇒ a = (v-u)/t
⇒ v = u + at
Second Equation: s = ut + ½ at2
Distance traveled by object = Area of OABC (trapezium)
= Area of OADC (rectangle) + Area of ∆ABD
= OA × AD + ½ × AD × BD
= u × t + ½ × t × (v – u)
= ut + ½ × t × at
⇒ s = ut + ½ at2 (∵a = (v-u)/t)
Third Equation: v2 = u2 + 2as
s = Area of trapezium OABC
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1. What is the difference between distance and displacement in motion? |
2. How can uniform and non-uniform motion be distinguished? |
3. How is speed with direction different from just speed in motion? |
4. How can the rate of change of velocity be calculated in motion? |
5. What are the equations of motion and how are they used in analyzing motion? |
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