Question

What is the angle between instantaneous displacement and acceleration during the retarded motion?
A. Zero
B. $\pi$
C. $\dfrac{\pi }{2}$
D. $\dfrac{\pi }{4}$

Answer 1

To solve these types of questions we need to understand how displacement and acceleration are related to each other. Now also note that it is said that we are retarding the motion, thus we have to consider the acceleration in the opposite direction. Instantaneous displacement is denoted as $x$and acceleration is denoted as $a$ .

Complete answer:
We consider the direction of both displacement and acceleration in the same direction, this is because the acceleration is applied in the direction of motion. Now we know that acceleration and retardation are just opposite in direction. Thus, we can easily say that during retardation, the direction of acceleration is just opposite to that of motion.
Now note that if both the motion and the acceleration are in the same direction then they should be parallel, or we can say that they are at zero degree to each other as angle between parallel lines is zero. Now from the question we get the idea that acceleration and displacement are just opposite to each other, hence they can be said to be parallel but they are in opposite directions. Hence the angle between them is $\pi$ or they are at ${180^o}$ to each other.

Note:
It is important to note that in each of the questions related to direction, we have to consider the required angle as relative to a given point or quantity (As here we consider the direction of acceleration relative to the given direction of motion). Also, we should read the question well to understand what kind of motion is taking place here, as if it was rotational, the answer would be completely different to rectilinear motion.