Question

Four cars A, B, C and D are moving on a leveled road. Their distance versus time graphs are shown in the figure. Choose the correct statement

a) Car A is faster than car D
b) Car B is the slowest
c) Car D is faster than C
d) Car C is the slowest

Answer 1

Hint: In the above question the velocity time distance time graph of different cars is given to us. The velocity of the car is given by the ratio of distance covered to that of the unit time. In the above graph this corresponds to the slope of the line corresponding to the various cars. Hence comparing the slopes of various line graphs of cars will enable us to select the correct alternatives.
Formula used:
$v=\dfrac{\Delta x}{\Delta t}$

Complete step by step answer:
Let us say a car covers a distance $\Delta x$ in time $\Delta t$. Then the velocity ‘v’ of the car is given by,
$v=\dfrac{\Delta x}{\Delta t}$
The above result can be interpreted on a distance time graph as the slope of the line. Greater the slope of the line greater is the velocity and smaller the slope of the line graph of the corresponding car, slower is the velocity of the car. In the above question the increasing order of the slopes of the line graph of cars is,
$BHence from the above conclusion we can imply that the speed of the car C is maximum and the speed of car B is minimum.

So, the correct answer is “Option b”.

Note: The slope of the line graph is nothing but the ratio of the change in the y coordinates of the graph to that of the change in the x coordinate of the graph. In the above graph the y-axis represents the distance covered and the x-axis represents the time taken. Since the ratio considering this coordinate axis is nothing but the velocity, we can imply that the slopes of the above graph gives us the idea of the velocity of the cars.