Question

four cars a,b,c and d are moving on a levelled straight road. Their distance time graph are shown in the figure below. Which of the following is the correct statement regarding the motion of these cars.
(1) car a is faster than car d
(2) car b is the slowest
(3) car d is faster than car c
(4) car c is the slowest​

Answer 1

Answer:

car b is the slowest

Explanation:

The slope of distance-time graph represents the speed. From the graph, it is clear that the slope of distance-time graph for car B is less than all other cars. So, the slope is minimum for car B. Hence, car B is the slowest.

Answer 2

The car B is the slowest. hence option (2) is correct.

Four cars ; a , b , c and d are moving on a levelled straight road. Their distance - time graph are shown in the figure below.

Which of the following is the correct statement regarding the motion of these cars ?

1. car A is faster than car D.
2. car B is the slowest.
3. car D is faster than car C.
4. car C is the slowest.

Concepts :

• If we draw distance - time graph of an object, then the slope of graph shows the speed of that object.
• We know, slope of a straight line is the tangent of angle of positive direction of the straight line with the x - axis . i.e., slope = tanФ , where Ф is the  angle made by graph in positive direction with x - axis.
• tanФ is increasing function between 0 to 90°. means, higher the value of Ф, higher the value of tanФ will be.

Here, It is clear with the diagram shown in the figure below,

angle made by graph of car C > angle made by graph of car D > angle made by graph of car A > angle made by graph of car B

$\implies\theta_C > \theta_D > \theta_A > \theta_B\\\\\implies tan\theta_C > tan\theta_D > tan\theta_A > tan\theta_B\\\\\implies v_C > v_D > v_A > v_B$

Therefore it is clear that the car B is the slowest.

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