Question

Assume a truck enters a highway at time t = 0 s at 40 mph, and a car enters the highway at time t=20 s at 60 mph.

(a) Compute the time when the spacing between the car and the truck is 500ft, assuming the car is behind the truck.

(b) How far from the entrance will each vehicle be when the headway (time separation) between the truck and the car is 10s? You can still assume the car is behind the truck.

If possible please say where you get the equations for these from

Answer 1

Speed of truck =40 mph speed of car=60 mph

Time of start =0 sec Time of start =20 sec

Gap between truck and car at T=20 sec is

Relative speed between car and truck =60-40=20 mph= 88/3 ft / sec

Time when spacing is 500 ft =

Distance that can be covered in 10 sec =

time required to get 10 sec headway =

Time from start for truck when time headway is 10 sec =50 sec

Total distance travelled by truck =

Total running time of car when time headway is 10 sec = 30 sec

Total distance of car travelled =