2005

1. (a)    Car A and car B travel in the same direction along a horizontal straight road.
Each car is travelling at a uniform speed of 20 m/s.
Car A is at a distance of d metres in front of car B.
At a certain instant car A starts to brake with a constant retardation of 6 m/s².
0.5 s later car B starts to brake with a constant retardation of 3 m/s² .

Find

(i) the distance travelled by car A before it comes to rest

(ii) the minimum value of d for car B not to collide with car A.

 

Answer

1 (a) (i) How far does car A travel?
    No “t”:   i.e. 0² = 20²+2(-6)s  i.e. s = 33.3 m

(ii)

In 0.5 seconds car B travels ut = 20x0.5 = 10m
Car B then continues to move while decelerating:
    No “t”:   i.e. 0² = 20²+2(-6)s  i.e. s = 66.7 m.

Thus car B has moved a total distance of 10+66.7 = 76.7 m

To just avoid collision:

the distance travelled by car B = d + distance travelled by car A

i.e. 76.6 = d + 33.3 i.e. d = 46.7 m.