The variation of quantity \(A\) with quantity \(B\) is plotted in the given figure which describes the motion of a particle in a straight line.
Consider the following statements:
| a. | Quantity \(B\) may represent time. |
| b. | Quantity \(A\) is velocity if motion is uniform. |
| c. | Quantity \(A\) is displacement if motion is uniform. |
| d. | Quantity \(A\) is velocity if motion is uniformly accelerated. |
Select the correct option:
1. (a, b, c)
2. (b, c, d)
3. (a, c, d)
4. (a, c)
Hint: Recall the concept of uniform motion and uniformly accelerated motion.
Step 1: Find the nature of the displacement-time graph in uniform motion.
When we are calculating the velocity of a displacement-time graph we have to take the slope. Similarly, we have to take the slope of the velocity-time graph to calculate acceleration.
Step 2: Find the nature of the velocity-time graph for uniformly accelerated motion.
When the slope is constant motion will be uniform. When we are representing motion by a graph it may be displacement-time, velocity-time or acceleration-time hence, B may represent time. For uniform motion, the velocity-time graph should be a straight line parallel to the time axis. For uniform motion velocity is constant hence slope will be positive. Hence quantity A is displacement.
Therefore, for uniformly accelerated motion slope will be positive and A will represent velocity.
Hence, option (3) is the correct answer.
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