The driver of a car wishes to pass a truck that is traveling at a constant speed of 20.0 m/s (about 45 mi/h). Initially, the car is also traveling at 20.0 m/s, and its front bumper is 24.0 m behind the truck’s rear bumper. The car accelerates at a constant 0.600 m/s2, then pulls back into the truck’s lane when the rear of the car is 26.0 m ahead of the front of the truck. The car is 4.5 m long, and the truck is 21.0 m long. (a) How much time is required for the car to pass the truck? (b) What distance does the car travel during this time? (c) What is the final speed of the car?

The total distance (relative to the truck) that the (front bumper of the) car travels from 24m behind the truck's rear bumper to in front of the car is

distance from car's front bumper to the truck's rear bumper + distance from truck's rear bumper to truck's front bumper (truck's length) + distance from truck's front bumper to car's rear bumper's + distance from the car's rear bumper to the car's front bumper (car's length)

= 24 + 21 + 26 + 4.5 = 75.5 m

As they start at the same speed, we can draw the following equation of motion for the car distance relative to the truck

[tex]s = at^2/2[/tex]

[tex]75.5 = 0.6t^2/2[/tex]

[tex]t^2 = 251.67[/tex]

[tex]t = \sqrt{251.67} = 15.864s[/tex]

b) The actual distance relative to Earth that the car has traveled during this time is the distance car traveled relative to the truck plus distance truck traveled relative to Earth within this time

= 75.5 + 20*15.864 = 392.78 m

c) final speed of the car is the initial speed plus the change in speed

[tex]v = v_0 + \Delta v = v_0 + at = 20 + 15.864*0.6 = 29.52 m/s[/tex]