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?
- 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?
Solution and Explanation
(a) Object B
\(Speed = \frac{Distance }{ Time}\)
= \(Slope \;of \;graph = \frac{y - axis }{ x - axis}\)
= \(\frac{Distance }{ Time}\)
Therefore, Speed = slope of the graph
Since slope of object B is greater than objects A and C, it is travelling the fastest.
(b) No
All three objects A, B and C never meet at a single point.
Thus, they were never at the same point on road. 
(c) 5.714 km
On the distance axis: \(7\) small boxes = \(4\) \(km\)
Therefore,\(1\) small box = \(\frac{4 }{ 7}\) \(Km\)
Initially, object C is 4 blocks away from the origin.
Therefore, Initial distance of object C from origin = \(\frac{16 }{ 7}\) \(Km\)
Distance of object C from origin when B passes A = \(8\) \(km\) Distance covered by C.
(d) 5.143 km
Position of B at the instant it passes C is, \(4+2×0.57=5.14 \;km\)
∴ Distance traveled by B = \(5.14−0=5.14 \;km\)
Top Questions on Graphical Representation of Motion
- A driver of a car travelling at \(52\) \(km \;h^{–1}\) applies the brakes Shade the area on the graph that represents the distance travelled by the car during the period. (b) Which part of the graph represents uniform motion of the car?
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- Tissue that transports food in plants.
- Tissue that stores fat in our body.
- Connective tissue with a fluid matrix.
- Tissue present in the brain.
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Use these adverbs to fill in the blanks in the sentences below.
awfully sorrowfully completely loftily carefully differently quickly nonchalantly(i) The report must be read ________ so that performance can be improved.
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(iii) We all behave _________ when we are tired or hungry.
(iv) The teacher shook her head ________ when Ravi lied to her.
(v) I ________ forgot about it.
(vi) When I complimented Revathi on her success, she just smiled ________ and turned away.
(vii) The President of the Company is ________ busy and will not be able to meet you.
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(Street Plan) : A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.
All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines. There are many cross- streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : If the 2nd street running in the North - South direction and 5th in the East - West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:
(i) how many cross - streets can be referred to as (4, 3).
(ii) how many cross - streets can be referred to as (3, 4).
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(i) a yellow wood
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(iii) the passing there
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Concepts Used:
Distance and Displacement
Distance:
The sum of the length of the path traveled by an object from one place to another is called distance. The path may or may not be directly from the initial point to the final point.
Distance is a scalar quantity and has only magnitude, also does not have any direction.
For example,
From the particular point, if a car travels to the east for 5 km and takes a turn to travel north for another 8 km, the total distance traveled by car shall be 13 km. The distance can never be zero or negative but should be always more than the displacement of the object. The distance of the object gives complete information about the path traveled by the object.
Read More: Difference between Distance and Displacement
Displacement:
The length of the shortest path from the initial point to the final point is called displacement. It is a vector quantity that consists of magnitude as well as direction.
For example,
Let's consider the same example given above, the total displacement of the object will be the length of the line joining the two positions. The displacement of an object is usually shorter or equal to the distance traveled by the object. The displacement of the object does not give the proper information about the path traveled by the object.