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Uniformly accelerated motion
Jun 10, 2025
learn about Uniformly accelerated motion
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in this video we will deal with
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uniformly accelerated motion most of the
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Motions that we came across in daily
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life is non-uniform motion either things
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are speeding up or they are slowing down
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in non-uniform motion the velocity of
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the body changes as the motion proceeds
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which means the velocity of the body
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keeps changing with the passage of time
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and such a body is set to have
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acceleration now potion with constant
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acceleration or uniformly accelerated
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motion is that in which velocity changes
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at same rate throughout the motion means
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a isal to DV upon DT which is change in
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velocity with the passage of
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time is
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constant now when acceleration of the
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moving object is constant it's average
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acceleration and instantaneous
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acceleration they both are equal so we
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have average
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acceleration equals to instantaneous
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acceleration that is equals to V2 -
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V1 on T2 - T1 where V1 is the initial
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velocity at some time interval T and V2
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is final velocity of the particle at the
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time interval T2 now to discuss further
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let us consider V
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not be the velocity of particle at some
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initial time say T1 = t =
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0 and VB the velocity of particle at
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time
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T2 is equal to
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T now let us number this equation as
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equation one now if we put these values
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in this equation one then we have
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acceleration a = to vus
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V upon T minus t or we have v = v + a t
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let us number this equation as number
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two now this is the velocity time graph
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for reanal motion with constant
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acceleration and from this graph it is
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clear that velocity V at any time T is
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equals to initial velocity plus the
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change in velocity that is 8 so V is
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equals to this velocity V which is the
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initial velocity and change in velocity
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that is equals to 8 which we see here in
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this relation so similarly average
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velocity can also be written as V = to x
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-
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x upon t - 0 where this x not is the
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position of object at time T is equal to
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0 and V this V bar is the average
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velocity between time t equal to 0 to
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time t
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solving this equation for x we get x = x
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+ V T now we know that in interval from
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T is = to 0 to T the average velocity is
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given
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as and now putting this
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equation 2 we
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get and now putting this in equation
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three we
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[Music]
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get and this is the position time
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relation for object moving with
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uniformly accelerated
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motion and now from equation this
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equation five it is clear that an object
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at any time T has quadratic dependence
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on time when it is moving with constant
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acceleration along a straight line and
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position time graph for such a motion
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will be parabolic in nature so this is
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the position time graph of a particle
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moving with uniformly accelerated motion
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now this equation 5 and equation
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are the basic equations of constant
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acceleration and these two equations can
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be combined to get yet another relation
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for x v and a in which we can eliminate
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T now so
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putting T is equal
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to vus V by
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a using this equation
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2 and putting this relation for T in
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equation five and solving for V find
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v² =
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v² + 2 a x -
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x so this is equation 6 now from this
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equation 6 we can clearly see that it is
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a velocity dependent relation between
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velocities of the object moving with
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constant acceleration at time T and T is
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equal to 0 and their corresponding
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positions at that instant of time and
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this
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is and this relation is very useful in
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solving problems when we do not know
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anything about
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time T likewise we can also eliminate
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the acceleration a between equation 2
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and 5 from this relation we have a = to
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v- V upon
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T now putting
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this in equation
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5 we
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get x -
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x is = to v t + 1 by
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2 V - V upon
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T into
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t² so let me label this equation as
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equation number seven and this relation
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is helpful when we do not know about
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acceler
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with which the particle is moving
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similarly we can also eliminate V not
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using equation 2 and 5 so what are
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equations 2 and five they
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are this is equation 2 and the equation
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5
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is now again from equation 2 we have V
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is equal to v- a now putting this
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value of v in equation 5 and solving it
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for x - x we
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find VT - 1X 2 a
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t² so this equation does not involve
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initial velocity th this these basic
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equations 2 5 and derived equations 6 7
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and 8
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then let me
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[Music]
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write so these basic equations 2 five
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and derived equation these 6 7 and 8 can
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be used to solve constant acceleration
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problems now we will discuss what is
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free fall acceleration the freely
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falling motion of any body under the
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effect of gravity is an example of
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uniformally accelerated motion now
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kinematic equations of motion under
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Gravity can be obtained by replacing
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acceleration a in uh the previous
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equations of motion by the letter G
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where G is
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acceleration due to gravity
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and the value of G is equal to
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9.8 m/s squ now chematic equations of
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motion for object moving under the
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action of gravity
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are v = v +
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GT now X = to v t + 1 by 2 GT
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² and V sare - v² equal to 2 g
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x the value of G is taken as positive
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when the body falls vertically downwards
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and its value is taken as negative when
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the body is projected up against the
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gravity so this is all for now in our
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next video we will discuss about
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relative velocity
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