Question

A particle moves along a straight line with uniformly increasing acceleration. In the first 2 seconds, it covers 10 meters, and in the next 2 seconds it covers 30 meters. Which of the following statements is correct?

• A. The particle has a constant velocity.
• B. The particle's acceleration is increasing linearly with time.
• C. The particle has a constant non-zero acceleration, and the initial velocity is non-zero.
• D. The particle starts from rest and has constant acceleration.

Hint:

For a particle with uniformly increasing acceleration, the distance covered in successive intervals will not be constant. It indicates that the velocity is increasing, and hence acceleration is not constant, but can still be analyzed using kinematic equations for constant acceleration.

Answer 1

The Correct Option is D

The particle is experiencing uniformly increasing acceleration, meaning the acceleration is not constant. The distance traveled in the first 2 seconds is 10 meters, and in the next 2 seconds, it covers 30 meters. This indicates that the distance covered in the second interval is greater than the first, suggesting that the velocity is increasing, and therefore, the acceleration must be increasing as well. This implies the particle is not moving with constant velocity or constant acceleration.
Now, analyzing the correct answer:
- The statement "The particle starts from rest and has constant acceleration" makes sense, as the problem describes motion with increasing acceleration. Given the conditions, the particle must have started from rest (initial velocity is zero) and had constant acceleration for the motion described.
Thus, the correct answer is that the particle starts from rest and has constant acceleration. This is supported by the fact that the particle’s motion adheres to the equation \( s = ut + \frac{1}{2}at^2 \) where \( u = 0 \), and the distance increases in a way that supports constant acceleration.
- Option (1) is incorrect because the particle does not have constant velocity (its velocity is increasing).
- Option (2) is incorrect as the acceleration is increasing, not constant.
- Option (3) is incorrect because constant acceleration was mentioned, not varying.
Hence, the correct answer is that the particle starts from rest and has constant acceleration.