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PS112: Physics By Somchai Thangsathityangkul Lecture 4: One dimension motion (Continue)

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2 Constant velocity motion An object move with an uniform motion slope of x(t) = constant

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3 Acceleration

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6 EXAMPLE

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8 Constant Acceleration For constant a(t) = a = if object is at x 0 at time t 0 after an elapsed tim t it will be at

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9 Constant Acceleration Since v(t) increases uniformly with t

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10 Constant Acceleration We have So, Then,

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11 Constant Acceleration Using calculus :

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13 Example How long does it take a car to travel 30 m if it accelerates from rest at a rate of 2.0 m/s 2 ? Solution: Known x 0 = 0, v 0 = 0, a = 2.0 m/s 2, x=30 m t = ? from eq :

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14 Example Particle is at the coordinate position x 0 =5m at t=0 and moving with a velocity v 0 =20 m/s. The particle then starts to decelerate. At t=10 s the particle has a velocity v=2 m/s a) What is the acceleration ? b) What is the position function ? c) How long is it before the particle returns to x=5m.

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17 EXAMPLE A car traveling at a constant speed of 45.0 m/s passes a trooper hidden behind a billboard. One second after the speeding car passes the billboard, the trooper sets out from the billboard to catch it, accelerating at a constant rate of 3.00 m/s 2. How long does it take her to overtake the car?

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19 Try this An alpha particle travels along the inside of a straight hollow tube 2.0 m long which forms part of a particle accelerator. a) If one assumes uniform acceleration, what is the acceleration of the particle, if it enters at a speed of 1.0x10 4 m/s and leaves at 5.0x10 6 m/s ? b) How long is it in the tube ?

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20 Try this You break your car from a velocity of 85 km/hr to 45 km/hr over a distance of 105 m. a) What is the acceleration ? b) How much time elapses during this interval ? c) If you were to continue braking with the same acceleration, how much longer would it take for you to stop and how much additional distance would you cover ?

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