Question

3 cars are moving on the same straight line carA with velocity 36 km/hr and carB and C with 54km/hr in opp direction at an instance when the distance AB is equal to distance AC both being 1km carB decides to overtake carA before carC does. what minimum accn of car B is required to avoid collision?​

Answer 1

Answer: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