On a two lane road, car A is travelling with a speed of 36km/h . two cars B and C approach car A in opposite directions with a speed of 54km/h each. At certain instant ,when the distance AB is equal to AC , both being 1 km , B decides to overtake A before C does. what minimum acceleration of car B is required to avoid an accident ?
Suppose car A, B and C are moving with speeds VA, VB and VC respectively. Let the positive direction of X-axis be taken in the direction of motion of car A and car B. Now VA= 36km/h and VB=54km/h and VC= -54km/h.
Now the relative velocity of car B with car A is
VBA= VB-VA = 54 – 36= 18km/h
Relative velocity of car C with respect to car A is
VCA = VC- VA = -54-36 = -90km/h
Negative sign shows VCA is along negative X- axis.
Now suppose the car C takes time t to cover the distance BA of 1km in slightly less than (1/90)h at a speed VBA= 18km/h
Substituting u= 18km/h , t=1/90 h and S= 1 km in the formula
S= ut +1/2at2
We have 1000= 5x40 + ½ a x (40)2
800a = 1000 – 200
a = 800/800 =1m/s2