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 19.8 m/s . Initially, the car is also traveling at a speed 19.8 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 0.550 m/s2 , then pulls back into the truck's lane when the rear of the car is a distance 26.5 m ahead of the front of the truck. The car is of length 4.60 m and the truck is of length 22.0 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

Here,

speed of truck , vt = 19.8 m/s

initial speed of car , vc = 19.8 m/s

distance , d = 24.3 m

acceleration , a = 0.55 m/s^2

total distance travelled by car , D = 26.5 + 22 + 4.6 + 24.3

D = 77.4 m

total time taken is t

Using second equation of motion

D = 0.5 * a * t^2

77.4 = 0.5 * 0.55 * t^2

solving for t

t = 16.8 s

the tima required for the car to pass truck is 16.8 s
-------------------------------

distance tarvelled by car = initial speed of car * time + D

distance tarvelled by car = 19.8 * 16.8 + 77.4

distance tarvelled by car = 409.6 m

the distance tarvelled by car is 409.6 m

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final speed of car = vt + a * t

final speed of car = 19.8 + 0.55 * 16.8

final speed of car = 29 m/s

the final speed of car is 29 m/s

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