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,

$\text{Velocity} = \dfrac{\text{displacement}}{\text{time}}$

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

At t = 4 h

Car A

$\text {Velocity} = \dfrac {160 - 0 \text {km}}{4 - 0 \text {h}} \\[0.5em] \Rightarrow \text {Velocity} = \dfrac {160 \text {km}}{4 \text {h}} \\[0.5em] \Rightarrow \text {Velocity} = 40 {\text {kmh}}^{-1} \\[0.5em]$

Hence, velocity of car A = 40 km h^-1

Car B

$\text {Velocity} = \dfrac {120 - 40 \text {km}}{4 - 0 \text {h}} \\[0.5em] \Rightarrow \text {Velocity} = \dfrac {80 \text {km}}{4 \text {h}} \\[0.5em] \Rightarrow \text {Velocity} = 20 {\text {kmh}}^{-1} \\[0.5em]$

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

When we observe the graph, we find that both cars A and B intersect at a point K.

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.