Question

The graph shows the position of two cars A and B as a function of time. The cars move along the X axis on parallel but separate tracks. At which instant is car A overtaking car B?

A. \[{{t}_{1}}\]
B. \[{{t}_{2}}\]
C. \[{{t}_{3}}\]
D. \[{{t}_{4}}\]

Answer 1

Hint: In this question we have been asked to find the instant or the time a which the given car A overtakes the car B. We have been given a graph representing positions of the two cars. We know that, when a car overtakes another car, the position of two cars is different. The car overtaking will cover greater distance at the instant than the car that is being overtaken. Therefore, from the given graph we shall find the instant when the car A has covered greater distance than car B.

Complete step by step answer:
In the given diagram, at the first instant i.e. \[{{t}_{1}}\] the car A and car B have equal distance covered. Therefore, both the cars will be moving parallel to each other covering equal distance from rest to the first instant.
Similarly, in the third instance i.e. \[{{t}_{3}}\], again both the cars have covered equal distance from rest to the third instance.
Now, at the last interval the position of car B is ahead of car A. Therefore, car A has been overtaken by car B, as it has covered greater distance than car B.
But, at the second interval. The position of car A is ahead of car B. At the second interval the car A covered more distance than car B. Therefore, it is at this instant that car A will have overtaken car B.

Therefore, the correct answer is option B.

Note:
A motion of a body can be defined or represented by a position versus time graph. This graph plots positions relative to origin on Y axis and time on the X axis. When the slope of the position-time graph is calculated, we get the value of velocity. Velocity is given as position or displacement over time and the slope of a graph is given as a point on Y axis over X axis. The steeper the slope, faster is the speed of the body.