In the following displacement (x) vs time (t) graph, at which among the points P, Q and R is the object's speed increasing.

(A) R only
(B) P only
(C) Q and R only
(D) P, Q, R

Hint: Use the information that the object's velocity depends on the slope of the curve, which is placed on the displacement vs time graph. We can determine the correct answer from the given option. If the curve's variation is zero, it becomes straight. In this condition, the object's velocity also becomes uniform.

Complete step by step answer:
We know that the displacement of the object gives information about the velocity of the object. So, to observe the object's motion during the traveling, we generally plot the graph between object displacement and time. The variation of the curve in the graph will give information about the velocity of the object. The curve's slope is used to determine whether the graph's speed or velocity increases or decreases because a change in displacement of the object with time is known as the curve slope.In the given figure, we can see that the variation occurs at the curve's various points, so the slope of the curve is also different at different points. At point P, and Q, we can say that the curve slope is decreasing or tends to decrease after some time. So, if the slope is decreasing, it means that the object's speed is also decreasing. But at point R, the slope is increasing at a high rate, so the object's speed also increases.
Therefore, the object's speed increasing at point R and option (A) is correct.

Note: The curve's slope is used to determine whether the object's speed or velocity increases or decreases during the traveling because a change in displacement of the object with time is known as the slope. If the object's displacement is large, then the slope of the curve increases and results in high object velocity.