標題:
Mechanics
發問:
(1) A car A traveling at 18 km/h along a straight road observes a carB, 120 m ahead, traveling at 45 km/h in the same direction. A acceleratesuniformly and overtakes B, after B has traveled 1 km. Calculate the speed of the car A at the instant itovertakes B and also the uniform acceleration of A.(2) A car... 顯示更多 (1) A car A traveling at 18 km/h along a straight road observes a carB, 120 m ahead, traveling at 45 km/h in the same direction. A acceleratesuniformly and overtakes B, after B has traveled 1 km. Calculate the speed of the car A at the instant itovertakes B and also the uniform acceleration of A. (2) A car traveling with uniformacceleration is observed to have velocities of 27 km/h and 81 km/h at the beginning and end of a measureddistance of 0.45 km. Howmuch farther must it travel before it attains a speed of 108 km/h?
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1. 18 km/h = 5 m/s, 45 km/h = 12.5 m/s Let T be the time taken for car A to overtake car B Consider car B, 1000 = 12.5T T = 1000/12.5 s = 80 s Consider car A, use equation of motion: s = ut + (1/2)at^2 with s = (1000 + 120) m = 1120 m, t = 80s, u = 5 m/s, a =? hence, 1120 = 5 x 80 +(1/2)a(80^2) i.e. a = 0.225 m/s2 Velocity of car A when it overtakes car B =( 5 + 0.225 x 80) m/s = 23 m/s 2. Consider the travelling distance of 0.45 km. Use equation of motion: v^2 = u^2 + 2a.s with u = 27 km/h(=7.5 m/s), v = 81 km/h(=22.5 m/s) s = 0.45 km(= 450 m), a = ? hence, 22.5^2 = 7.5^2 + 2a(450) a = 0.5 m/s2 Apply the equation of motion: v^2 = u^2 + 2as with u = 22.5 m/s, v = 108 km/h(=30 m/s), a = 0.5 m/s2, s =? hence, 30^2 = 22.5^2 + 2.(0.5)s s = 394 m Therefore, the car needs to travel 394m before attaining the speed of 108 km/h
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