Question

At time $ {t_3} $ ​ which car is moving faster?

(A) Car A
(B) Car B
(C) Same speed
(D) None of these

Answer 1

Hint: From the given graph find the slope of both the cars $ {t_3} $ . With the concept that the more the slope at an instant more is the velocity of the given object, we will find which car is moving faster in the given question.

Complete answer:
The given 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 so that they can pass without colliding with each other

We have a position versus time graph so we know velocity
 $ v = \dfrac{{dx}}{{dt}} $ is equal to the slope of this position-time graph.
. We can see that the slope of B at the same moment $ {t_3} $ is greater than that of A if we draw a tangent to the graph of A $ {t_3} $ and use it to measure its slope. The velocity is now determined by the slope of a Displacement/Position-Time graph. As a result, at moment $ {t_3} $ , B's velocity is greater than A's.
So the slope of B $ > $ slope of A
Therefore, the velocity of B $ > $ velocity of A
Hence option B) car B is the correct option.

Note:
The instantaneous velocity is a statistic that tells us how fast an object is going somewhere along its route. It's the average velocity between two places on a path in the limit when the time (and thus the distance) between them approaches zero. A tangent drawn to the graph of A is parallel to the tangent of B at an instant $ {t_2} $ . As a result, their slopes are identical, as are their velocities.