The figure drawn below gives the velocity graphs of two vehicles A and B

The figure drawn below gives the velocity graphs of two vehicles A and B. The straight line OKP represents the velocity of vehicle A at any instant, whereas the horizontal straight line CKD represents the velocity of vehicle B at any instant. In the figure, D is the point where perpendicular from P meets the horizontal line CKD such that PD = ½ LD:

What is the ratio between the distances covered by vehicles A and B in the time interval OL?

  1. 1 : 2
  2. 2 : 3
  3. 3 : 4
  4. 1 : 1

Answer

Distance = Velocity × Time

So, the area under velocity-time graph gives the distance. In the time interval OL,

Distance covered by vehicle B = area of rectangle COLD = OL × LD

Distance covered by vehicle A = area of triangle POL = ½ OL × PL

=  ½ OL × (PD + LD)

=  ½ OL × (½LD + LD)

= 3/4 OL × LD

The correct option is C.