Answer to Question #160109 in Physics for Kennedy Gilbertson

Question

The driver of a car wishes to pass a truck that is traveling at a constant speed of 20.0 m/s. Initially, the car is traveling at a speed 25.0 m/s and its front bumper is a distance 24.0 m behind the truck's rear bumper. The car begins accelerating at a constant acceleration 0.6 m/s2, then pulls back into the truck's lane when the rear of the car is a distance 26.0 m ahead of the front of the truck. The car is of length 4.00 m and the truck is of length 21.0 m.

The following 3 questions are all referenced to the above text. 

How much time does it take for the car to pass the truck? Note, the complete 'passing' is defined as the moment when the car pulls back into the truck's lane with 26.0m distance between the car and the truck.

Answer 1

$$x_c-x_t=d=v_ct+0.5at^2-x_0-v_tt\\26=25t+0.5(0.6)t^2-24-20t\\t=7.0\ s$$