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PS112: Physics By Somchai Thangsathityangkul Lecture 4: One dimension motion (Continue) Constant velocity motion An object move with an uniform motion slope of x(t) = constant v = v(t) = v 0 , x = x 0 at t= 0 at an y tim e t p o sitio n is at x (t) v = v0 = x (t) - x 0 t-0 x (t) = x 0 + v 0 t 2 Acceleration 3 4 5 EXAMPLE 6 7 Constant Acceleration For constant a(t) = a = v (t ) v0 t0 , v v 0 at t = 0 v ( t ) v 0 at if object is at x0 at time t0 after an elapsed tim t it will be at x x 0 vt 8 Constant Acceleration Since v(t) increases uniformly with t v v0 v (t ) x (t ) x0 2 x (t ) x0 t 1( v 0 v ( t )) t ( v0 v0 a t )t 2 2 (v0 x (t ) x0 v0t 1 at 1 a t )t 2 2 2 9 Constant Acceleration v (t ) v0 a t We have So, t Then , v v0 a , x (t ) x0 v0 ( v v0 ) a 1 2 a( v v0 ) 2 a v v 2 a ( x x0 ) 2 2 0 10 Constant Acceleration Using calculus : x (t ) x0 v0t v (t ) dx dt a (t ) dv 1 at 2 2 v0 a t a ( a is a co n stan t ) dt 11 12 Example How long does it take a car to travel 30 m if it accelerates from rest at a rate of 2.0 m/s2 ? Solution: Known x0 = 0, v0 = 0 , a = 2.0 m/s2, x=30 m t = ? from eq : x (t ) x0 v0t 1 at 2 2 3 0 m = 0 + (0 )t + 1 2t 2 2 t = 3 0 5 .5 s 13 Example Particle is at the coordinate position x0=5m at t=0 and moving with a velocity v0=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. 14 15 16 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/s2. How long does it take her to overtake the car? 17 18 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 1.0x104 m/s and leaves at 5.0x106 m/s ? b) How long is it in the tube ? 19 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 ? 20