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IIS “Enrico Mattei” San Donato Milanese Physics course Displacement–time equation of uniformly accelerated linear motion Teacher Laura Scarpa

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What happens when a car accelerates? What happens when a car goes downhill? We will study the mathematical relation between time and displacement.

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We will use an air track to reduce friction

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Air track works on the principles of an air cushion Air spreads out from the air vents and forms an air–cushion between the surface of the air track and the inner surface of a glider.

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We need a constant force acting on the glider To provide a constant force we will incline the track at a precise amount. a=g*h L L a

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The time measurement is taken by the two photo-gates placed over the air track The glider triggers the timer passing through the gates.

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The timer starts as soon as the glider moves v 0 = 0 m/s

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S (m) T (s) K (m/ s 2 ) K average (m/ s 2 ) 0,000 / 0,1000,9250,1170,097 0,2001,3730,106 0,3001,7360,100 0,4002,0360,096 0,5002,2760,097 0,6002,5670,091 0,7002,8180,088 0,8003,0300,087 0,9003,2140,087 Experimental results K=s/t 2

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Cartesian graph the experimental curve is a parable S(m) T(s)

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K =s/t 2 But what about the value of the constant K? a=g*h L Let ’s compare the two values. K = 0,097 m/s 2 g=9,8 m/s 2 h=3,2 cm L= 162 cm a = 0,194 m/s 2 K= 1 a 2

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So the displacement–time equation of uniformly accelerated linear motion is S = 1 at 2 2

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And if v 0 = 0 ? v 0 = 0 S = v 0 t + 1at 2 2

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IF WE MEASURE DISTANCE AND TIME, WE GET:

IF WE MEASURE DISTANCE AND TIME, WE GET:

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