Which of the following is(are) example(s), which shows that a negative acceleration can be associated with a speeding up object? This question has multiple correct options A. an object in simple harmonic motion. B. water in a U-tube which is slightly disturbed C. a body on a rough horizontal plane. D. none of the above
Hint: Negative acceleration can be simply defined as the direction of the acceleration of the body is opposite to the direction of motion of the body. Analyse the given examples in the question and find out which process can have negative acceleration when speeding up.
Complete answer: Negative acceleration means the rate of change of acceleration per unit time is negative. If, as the time in increasing the acceleration of the body is decreasing, then we say that the body has negative acceleration.
So, negative acceleration means that the body is slowing down. But if the negative acceleration keeps acting on the body even after the velocity of the body reaches zero, then the body will move with a negative velocity. this negative velocity will increase if the negative acceleration still acts on the body. So, we can say that the body will speed up after the negative velocity is acting on the body.
Now, in case of simple harmonic motion when the article is moving away from the mean position, the restoring force on the particle is in the direction opposite to the direction of motion of the particle. So, the acceleration acting on the particle is negative acceleration. under negative acceleration, when the particle moves towards the mean position again, the particle will speed up.
Again, when water in a U-tube is displaced it will also exert simple harmonic motion. Soo, the water will also speed up under negative acceleration. The correct options are (A) and (B).
So, the correct answer is “Option A and B”.
Note: When the body is in a rough horizontal plane, no external force is acting on it to give the body acceleration. Since, the body will be at rest or the velocity of the body will be zero or constant, we can say that the body is not accelerating.