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Magnitude
Magnitude is the size or extent of a physical quantity. In physics, we have scalar and vector quantities.
Scalar quantities are only expressed as magnitude. E.g: time, distance, mass, temperature, area, volume
Vector quantities are expressed in magnitude as well as the direction of the object. E.g: Velocity, displacement, weight, momentum, force, acceleration, etc.
Time, Average Speed and VelocityTime and speed
Time is the duration of an event that is expressed in seconds. Most physical phenomena occur with respect to time. It is a scalar quantity.
Speed is the rate of change of distance. If a body covers a certain distance in a certain amount of time, its speed is given by
Speed=DistanceTime
Average speed = Total distance travelled / Total time taken
Uniform motion and non-uniform motion
When an object covers equal distances in equal intervals of time it is in uniform motion.
When an object covers unequal distances in equal intervals of time it is said to be in non-uniform motion.
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Velocity
The Rate of change of displacement is velocity. It is a vector quantity. Here the direction of motion is specified.
Velocity=DisplacementTime
Average velocity = (Initial Velocity + Final velocity)/2 = u+v2.
For More Information On Average Speed and Velocity, Watch The Below Video:
1,11,870
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Acceleration
The rate of change of velocity is called acceleration. It is a vector quantity. In non-uniform motion, velocity varies with time, i.e., change in velocity is not 0. It is denoted by “a”
Acceleration = Change in Velocity / Time
(OR)
a=v−ut
Where, t (time taken), v (final velocity) and u (initial velocity).
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Motion VisualisedDistance-Time graphDistance-Time graphs show the change in position of an object with respect to time.Linear variation = uniform motion and non-linear variations imply non- uniform motionThe slope gives us speedDistance – Time GraphOA implies uniform motion with constant speed as the slope is constantAB implies the body is at rest as the slope is zeroB to C is non-uniform motion
To know more about Distance-Time Graph, visit here.
Velocity-Time GraphVelocity-Time graphs show the change in velocity with respect to time.Slope gives accelerationThe area under the curve gives displacementLine parallel to x-axis implies constant velocity-Velocity – Time Graph
OA = constant acceleration, AB = constant velocity, BC = constant retardation
To know more about Velocity-Time Graph, visit here.
Equations of Motion
The motion of an object moving at uniform acceleration can be described with the help of three equations, namely
(i) v = u + at
(ii) v2 – u2 = 2as
(iii) s = ut + (1/2)at2
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Derivation of velocity-time relation by graphical methodVelocity – Time Graph
A body starts with some initial non-zero velocity at A and goes to B with constant acceleration a.
From the graph BD = v (final velocity) – DC = u (initial velocity)…………..(eq 1).
BD = BC – DC……………..(eq 2).
We know acceleration a = slope = BDAD or AD = OC = t (time taken to reach point B).
Therefore BD = at………………….(eq 3).
Substitute everything we get : at = v – u.
Rearrange to get v = u + at.
Derivation of position-time relation by graphical methodVelocity – Time Graph
A body starts with some initial non-zero velocity at A and goes to B with constant acceleration a
Area under the graph gives Displacement =A(ΔABD)+A(□OADC)=(12AD×BD)+OA×OC ……………(eq 1)
OA = u , OC = t and BD = at
Substituting in (eq 1) we get s= ut+12at2
Derivation of position-velocity relation by graphical methodVelocity – Time Graph
A body starts with some initial non-zero velocity at A and goes to B with constant acceleration a
Displacement covered will be the area under the curve which is the trapezium OABC.
We know the area of trapezium is s= (OA+BC)2∗OC
OA = u and BC = v and OC = t
Therefor, s= (v+u)2∗t ……………(eq 1)
We also know that t =(v−u)a ……………..(eq 2)
Substitute (eq 2) in (eq 1) and arrange to get
v2−u2=2as
Uniform Circular MotionUniform circular motionIf an object moves in a circular path with uniform speed, its motion is called uniform circular motion.Velocity is changing as direction keeps changing.Acceleration is constant
To know more about Uniform Circular Motion, visit here.
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