A car is a distance D directly behind a bus. Both the car and the bus are travel

Question

A car is a distance D directly behind a bus. Both the car and the bus are traveling at the same speed of 20.1 m/s (45 mi/h). In order to pass the bus the car moves over to the passing lane and accelerates to 29.1 m/s (65 mi/h) and then maintains that speed. A) If the car takes 3.40 s to get to 29.1 m/s, determine its acceleration (assume it is constant). B) Determine the distance that the car travels during the time that it accelerates. C) The total time for the car to catch up to the bus is 5.0 s. Determine the distance that the car travels while going at the constant speed of 29.1 m/s. D) What is the total distance that the car travels in the passing lane? E) Determine the distance D that the car was initially behind the bus.

Explanation / Answer

(a) Acceleration of car = ( final speed - initial speed ) / time

= ( 29.1 - 20.1 ) /3.4 = 2.647 m/s^2

(b) distance travelled = ( v^2 - u^2 ) / 2a = ( 29.1^2 - 20.1^2 ) / (2*2.647) = 83.64 m

(c) car moved at a constant velocity for 5 - 3.4 = 1.6 s

  distance that the car travels while going at the constant speed of 29.1 m/s = 29.1 x 1.6 = 46.56 m

(d) total distance travelled in the passing lane = 83.64 + 46.56 =130.2 m

(e) Distance the car is behind the bus is the extra distance travelled by car while chasing

D = 130.2 - 20.1*5 = 29.7 m

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