S.O.S. Mathematics CyberBoard

Car A is traveling on a highway at a constant speed (VA)o= 100km/h and is 120m from the entrance of an access ramp when car B enters the acceleration lane at that point at a speed (VB)o =25 km/hr. Car B accelerates uniformly and enters the main traffic lane after traveling 70 m in 5s. It then continues to accelerate at the same rate until it reaches a speed of 100km/hr, which it then maintains. Determine the final distance between the two cars.

_________________
http://kids--poems.blogspot.com/

Car A is travelling on a highway at a constant speed of 100km/h and is 120m from the entrance of an access ramp.

100 km/h = 27.8 m/s

Car B enters the acceleration lane at that point at a speed of 25 km/hr

25 km/h = 6.95 m/s.

Car B accelerates uniformly and enters the main traffic lane after travelling 70 m in 5s.

It then continues to accelerate at the same rate until it reaches a speed of 100km/hr. which it then maintains.

Determine the final distance between the two cars.

CAR B

Ave, speed on the ramp

70 m / 5 s = 14 m/s

Final speed on the ramp

( 6.95 m/s + final speed) / 2 = 14 m/s

final speed = 21.05 m/s

acceleration on the ramp

(21.05 m/s – 6.95 m/s) / 5s = 2.82 m/s/s

time taken to reach top speed

(27.8 m/s – 6.95 m/s) / 2.82 m/s/s = 7.4 s

average speed

(6.95 m/s + 27.8 m/s) / 2 = 17.38 m/s

distance travelled

17.38 m/s x 7.4 s = 128.6 m

CAR A

Distance travelled

27.8 m/s x 7.4 s = 205.7 m

distance of A from B

120 m + 128.6 m – 205.7 m = 42.9 m