The driver of a car wishes to pass a truck that is traveling at a constant speed

Question

The driver of a car wishes to pass a truck that is traveling at a constant speed of 20.2 m/s. Initially, the car is also traveling at a speed 20.2 m/s and its front bumper is a distance 24.3 m behind the truck's rear bumper. The car begins accelerating at a constant acceleration 0.590 m/s^2, then pulls back into the truck's lane when the rear of the car is a distance 27.0 m ahead of the front of the truck. The car is of length 4.90 m and the truck is of length 20.2 m. How much time is required for the car to pass the truck? What distance does the car travel during this time? What is the final speed of the car?

Explanation / Answer

Assuming that Automan is driving the car (ie all lateral movements are at 90 degrees :) Let us say that the maneuver takes t seconds. The (front of the) car needs to travel 24m to catch up,, 21m to pass the truck and another 30.5 meters to cut in (=25+4.5) This is = 75.5 meters travelled. Since both vehicles are moving at initially the same speed, lets say they are stopped (relative to each other they are). S = ut + 1/2 a t^2 75.5 = 0 + 1/2 * 0.6 * t^2 t^2 = 252 t = 15.86 seconds to pass the car During this time in addition to the 75.5 meters the car (and truck) would travel the distance S = ut + 0 = 20*15.86 = 317.28 m Total distance travelled by car = 317.28+75.5 = 393m The final speed of the car would be v = u + 1/2 at = 20 + .3*15.86 =25 m/s (approximately)

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