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KINEMATICS

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DISTANCE AND DISPLACEMENT - DEFINITIONS DISTANCE is a numerical (scalar) description of how far apart objects are. – Distance is length of the path DISPLACEMENT is the distance moved in particular direction (vector quantity) Unit of both distance and displacement is the meter (m)

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DISTANCE VS DISPLACEMENT A B Distance s = 50 m Displacement s = 30 m

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SPEED AND VELOCITY - DEFINITIONS SPEED is distance travelled per unit time – Speed is scalar quantity VELOCITY is displacement per unit time – Velocity is vector quantity Unit of both the speed and the velocity is the meter per second (ms -1 )

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AVERAGE AND INSTANTANEOUS VELOCITY Usually the body cannot travel with constant velocity. If we describe – the whole displacement of body and – whole time the body travelled, we can calculate AVERAGE VELOCITY of the body, AVERAGE VELOCITY describes average displacement of the body per unit time. If we broke our trip into lots of small pieces, we can consider each piece as the straight line travelled with constant velocity called INSTANTANEOUS VELOCITY. INSTANTANEOUS VELOCITY describes how fast the body going in that moment of time and in witch direction

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VELOCITY IS RELATIVE One body moves with different velocity consider different bodies. It means, that velocity is relative to body we measure the velocity.

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v’ = 15 ms -1 10 ms -1 u =10 ms -1 v= 0 ms -1 u´=? v’=15ms -1 10 ms -1 + 15 ms -1 = 25 ms -1 (to the right) u v Obs I Obs II

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v = 15 ms -1 10 ms -1 u=10 m/s v = 15 ms -1 u‘=? u v 10 ms -1 - 15 ms -1 = -5 ms -1 (to the right)

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RELATIVE VELOCITY If the velocities of bodies A and B are given as v A and v B, then the relative velocity of A with respect to B v ArelB (also called the velocity of A relative to B) is and the velocity of B relative to A is

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ACCELERATION ACCELERATION is the rate of change of velocity a – acceleration, v – the velocity at the end; u – the velocity in the beginning, t – time of changing velocity from u to v. Acceleration is a vector quantity The unit of acceleration is meter per second per second (ms -1 )s -1 or ms -2 If the velocity of the body reduces in time, then the acceleration of the body called as deceleration

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DISPLACEMENT AND ACCELERATION If body moves with constant acceleration we can calculate the velocity and displacement from equations:

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SIGN OF DISPLACEMENT, VELOCITY AND ACCELERATION All these quantities are vectors and the signs of these quantities describe their direction A POSITIVE displacement means that body has moved RIGHT A POSITIVE velocity means that body is moving to the RIGHT A POSITIVE acceleration means that the body either – moving to the RIGHT and getting FASTER or – moving to the LEFT and getting SLOWER or

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FREE FALL When body is allowed to fall freely, we say it is in free fall Bodies falling freely on the earth fall with acceleration of about g=9.81 ms -2 The body falls because of gravity, it means that direction of the vector g is always vertically down To calculate displacement, velocity etc we can use the same equations, we described, but we free falls acceleration g instead acceleration a.

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GRAPHICAL REPRESANTATION OF MOTION – DISTANCE-TIME GRAPHS Describe how changes: velocity: v=? acceleration: a=? Line A

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GRAPHICAL REPRESANTATION OF MOTION – DISTANCE-TIME GRAPHS Line B Describe how changes: velocity: v=? acceleration: a=?

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GRAPHICAL REPRESANTATION OF MOTION – DISTANCE-TIME GRAPHS Line C Describe how changes: velocity: v=? acceleration: a=?

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GRAPHICAL REPRESANTATION OF MOTION – DISTANCE-TIME GRAPHS Line D Describe how changes: velocity: v=? acceleration: a=?

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GRAPHICAL REPRESANTATION OF MOTION – VELOCITY-TIME GRAPHS v=0 ; a=0 v=const>0 ; a=0 v= const<0 ; a=0 a=const>0; v - increasing

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GRAPHICAL REPRESANTATION OF MOTION – ACCELERATION-TIME GRAPHS A; B; C – a=0 a = const > 0

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INSTANTANEOUS VELOCITY To find instantaneous velocity of constantly accelerating body, we draw tangent to the curve and find the gradient of the tangent – it is the same as velocity. ΔtΔt ΔsΔs

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AREA UNDER TIME-VELOCITY GRAPH area = v x Δt gives the displacement ΔtΔt v v = const > 0

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AREA UNDER TIME-VELOCITY GRAPH u Area1 = u x Δt ΔtΔt v

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AREA UNDER ACCELERATION-VELOCITY GRAPH area = a x Δt gives the change in velocity ΔtΔt a a = const > 0

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