Fig shows the distance-time graph of three objects A, B and C. Study the graph and answer the following questions:
Which of the three is travelling the fastest?
Are all three ever at the same point on the road?
How far has C travelled when B passes A?
How far has B travelled by the time it passes C?

Question

The speed-time graph for a car is shown is Fig.

Find how far does the car travel in the first 4 seconds. Shade the area on the graph that represents the distance travelled by the car during the period.
Which part of the graph represents uniform motion of the car?

Answer 1

Distance-Time Graph Analysis for Objects A, B, and C

Explanation:

The graph shows the distance traveled by three objects (A, B, and C) over time. From the distance-time graph, we can analyze the speed, relative positions, and distances traveled by these objects.

(i) Which of the three is traveling the fastest?

The object with the steepest slope on the distance-time graph is traveling the fastest because the slope represents the speed (rate of change of distance with respect to time). The steeper the slope, the faster the object is moving.

From the graph, it can be seen that **Object C** has the steepest slope, so **C is traveling the fastest**.

(ii) Are all three ever at the same point on the road?

The objects will be at the same point when their distance values are the same at a particular time. From the graph, we can observe that at some point, all three objects meet at the same distance (i.e., the lines intersect).

Yes, **all three objects are at the same point on the road** at a particular time when their distance values are equal.

(iii) How far has C traveled when B passes A?

The object that "passes" another will have a higher distance at the point of passing. To determine when **B passes A**, we need to find the point where the distance traveled by B is greater than that of A (where the distance-time lines of B and A intersect).

From the graph, we can observe that **B passes A at approximately 6 seconds**. At this time, **C has traveled approximately 12 meters** (as seen on the graph).

(iv) How far has B traveled by the time it passes C?

To determine when **B passes C**, we need to find the point where the distance traveled by B is equal to the distance traveled by C (where the lines of B and C intersect).

From the graph, **B passes C at approximately 9 seconds**. At this time, **B has traveled approximately 18 meters** (as seen on the graph).