Chapter02

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Unformatted text preview: greater than zero, we must choose t = 8.2 s as the proper answer. ( ) 1 1 2 (b) ∆x player = ( v i ) player t + aplayer t 2 = 0 + 4.0 m s 2 ( 8.2 s ) = 1.3 × 102 m 2 2 33 CHAPTER 2.40 2 Taking t = 0 when the car starts after the truck, the displacements of the vehicles from their initial positions at time t > 0 are: ( ) 1 1 ∆x car = ( v i ) car t + acar t 2 = 0 + 2.5 m s 2 t 2 , 2 2 and 1 ∆x truck = ( v i ) truck t + atruck t 2 = ( 40 km h ) t + 0 . 2 When the car overtakes the truck, ∆x car = ∆x t ruck , or ( ) 1 2.5 m s 2 t 2 = ( 40 km h ) t . 2 This has a solution t = 0 describing the initial situation and a second solution ⎡ ⎛ 0.278 m s ⎞ ⎤ 2 t= 40 k m h ) ⎜ 2 ⎢( ⎟ ⎥ = 8.9 s . 2.5 m s ⎢ ⎝ 1 km h ⎠ ⎥ ⎣ ⎦ The distance the car has traveled before catching the truck is ∆x car = + 2.41 ( ) 1 2 2.5 m s 2 ( 8.9 s ) = 99 m . 2 The distance the car travels at constant velocity, v 0 , during the reaction time is ( ∆x )1 = v 0 tr . The time for the car to come to rest, from initial velocity v 0 , after the brakes are applied v f − vi 0 − v0 v = = − 0 and the distance traveled during this braking period is is t 2 = a a a v2 ⎛ v f + vi ⎞ ⎛ 0 + v0 ⎞ ⎛ v0 ⎞ t2 = ⎜ − ⎟ =− 0 . ⎝ 2 ⎟⎜ a ⎠ ⎠⎝ 2a ⎝2⎟ ⎠ ( ∆x ) 2 = v t 2 = ⎜ Thus, the total distance traveled before coming to a stop is sst op = ( ∆x )1 + ( ∆x ) 2 = v 0 t r − 2 v0 . 2a 34 CHAPTER 2.42 2 2 v0 (See the solution to Problem 2.41) from the 2a intersection of length si when the light turns yellow, the distance the car must travel before the light turns red is (a) If a car is a distance sst op = v 0 t r − ∆x = sstop + si = v 0 t r − 2 v0 + si 2a Assume the driver does not accelerate in an attempt to “beat the light” (an extremely dangerous practice!). The time the light should remain yellow is then the time required for the car to travel distance ∆x at constant velocity v 0 . This is t light = 2 v s ∆x v 0 t r − v 0 2a + si =...
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This note was uploaded on 03/03/2010 for the course PHY P221 taught by Professor Dr.ha during the Spring '05 term at Indiana University South Bend.

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