2 DISTANCE AND DISPLACEMENT - DEFINITIONS DISTANCE is a numerical (scalar) description of how far apart objects are.Distance is length of the pathDISPLACEMENT is the distance moved in particular direction (vector quantity)Unit of both distance and displacement is the meter (m)
3 DISTANCE VS DISPLACEMENT s = 50 mDisplacements = 30 mB
4 SPEED AND VELOCITY - DEFINITIONS SPEED is distance travelled per unit timeSpeed is scalar quantityVELOCITY is displacement per unit timeVelocity is vector quantityUnit of both the speed and the velocity is the meter per second (ms-1)
5 AVERAGE AND INSTANTANEOUS VELOCITY Usually the body cannot travel with constant velocity. If we describethe whole displacement of body andwhole 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
6 VELOCITY IS RELATIVEOne body moves with different velocity consider different bodies.It means, that velocity is relative to body we measure the velocity.
7 10 ms-1 + 15 ms-1 = 25 ms-1 (to the right) u =10 ms-1v= 0 ms-1u´=?v’=15ms-1uObs I10 ms-1vv’ = 15 ms-1Obs II10 ms ms-1 = 25 ms-1 (to the right)
8 10 ms-1 - 15 ms-1 = -5 ms-1 (to the right) u=10 m/sv = 15 ms-1u‘=?u10 ms-1vv = 15 ms-110 ms ms-1 = -5 ms-1 (to the right)
9 RELATIVE VELOCITY If the velocities of bodies A and B are given as vA and vB, thenthe relative velocity of A with respect to B vArelB (also called the velocity of A relative to B) isand the velocity of B relative to A is
10 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 quantityThe unit of acceleration is meter per second per second (ms-1)s-1 or ms-2If the velocity of the body reduces in time, then the acceleration of the body called as deceleration
11 DISPLACEMENT AND ACCELERATION If body moves with constant acceleration we can calculate the velocity and displacement from equations:
12 SIGN OF DISPLACEMENT, VELOCITY AND ACCELERATION All these quantities are vectors and the signs of these quantities describe their directionA POSITIVE displacement means that body has moved RIGHTA POSITIVE velocity means that body is moving to the RIGHTA POSITIVE acceleration means that the body eithermoving to the RIGHT and getting FASTER ormoving to the LEFT and getting SLOWER or
13 FREE FALLWhen body is allowed to fall freely, we say it is in free fallBodies falling freely on the earth fall with acceleration of about g=9.81 ms-2The body falls because of gravity, it means that direction of the vector g is always vertically downTo calculate displacement, velocity etc we can use the same equations, we described, but we free falls acceleration g instead acceleration a.
14 GRAPHICAL REPRESANTATION OF MOTION – DISTANCE-TIME GRAPHS Line ADescribe how changes:velocity: v=?acceleration: a=?
15 GRAPHICAL REPRESANTATION OF MOTION – DISTANCE-TIME GRAPHS Line BDescribe how changes:velocity: v=?acceleration: a=?
16 GRAPHICAL REPRESANTATION OF MOTION – DISTANCE-TIME GRAPHS Line CDescribe how changes:velocity: v=?acceleration: a=?
17 GRAPHICAL REPRESANTATION OF MOTION – DISTANCE-TIME GRAPHS Line DDescribe how changes:velocity: v=?acceleration: a=?
18 GRAPHICAL REPRESANTATION OF MOTION – VELOCITY-TIME GRAPHS v=const>0 ; a=0a=const>0; v - increasingv=0 ; a=0v= const<0 ; a=0
19 GRAPHICAL REPRESANTATION OF MOTION – ACCELERATION-TIME GRAPHS a = const > 0A; B; C – a=0
20 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.
21 AREA UNDER TIME-VELOCITY GRAPH v = const > 0area = v x Δtgives the displacementvΔt
22 AREA UNDER TIME-VELOCITY GRAPH Area1 = u x ΔtvuΔt
23 AREA UNDER ACCELERATION-VELOCITY GRAPH a = const > 0area = a x Δtgives the change in velocityaΔt