Figure ahead represents the displacement-time sketch of motion of two cars A and B. Find — (i) The distance by which the car B was initially ahead of car A. (ii) The velocities of car A and car B (iii) The time in which car A catches car B (iv) The distance from start when the car A will catch the car B

(i) When we observe the graph, we find that the car B was ahead of car A by 40 km.

(ii) As we know,

Cars A and B have uniform velocities as displacement-time graph for both are straight lines.

At t = 4 h

Car A

Velocity = 160 - 0 \over 4 - 0

= 160 \over 4 

= 40 km h^-1

Hence, velocity of car A = 40 km h^-1

Car B

Velocity = 120 - 40 \over 4 - 0

= 80 \over 4 

= 20 km h^-1

Hence, the velocity of car A = 20 km h^-1

Hence,

(iii) the car A catches car B at time (t) = 2 h.

(iv) the distance from start when the car A will catch the car B = 80 km.