Two particles start simultaneously from origin and moves along +ve X-axis. One particle moves with uniform acceleration starting from the rest and second particle moves with constant velocity. The distance between them

The Correct answer is Continuously increases.

Key Points

• When a particle moves with uniform acceleration starting from rest, its velocity keeps increasing over time, and hence the distance covered increases quadratically.
• The second particle is moving with a constant velocity, meaning it covers equal distances in equal intervals of time.
• Initially, the particle with uniform acceleration lags behind as it starts from rest, while the particle with constant velocity moves ahead.
• As time progresses, the accelerated particle catches up in terms of velocity and overtakes the particle moving at constant velocity. However, the distance between them continuously increases as the accelerated particle moves further ahead.
• The mathematical equation for the distance covered by the particle with uniform acceleration is given by , where a is acceleration and t is time.
• For the particle moving at constant velocity, the distance covered is given by , where v is velocity and t is time.
• Comparing these distances, it becomes evident that the particle with uniform acceleration will eventually outpace the particle moving at constant velocity, and the gap between them will grow indefinitely over time.
• This scenario demonstrates the concept of relative motion and how different types of motion interact over time.

Additional Information

• If the distance between two particles does not change, it implies they are moving at the same velocity. However, in this case, one particle is accelerating while the other is moving at constant velocity, so the distance changes over time.
• First increases, decreases to zero and then increases: would occur only if the particle with uniform acceleration initially moves slower, reaches the same point as the constant velocity particle (distance becomes zero), and then overtakes it. However, in this scenario, the distance between them never decreases to zero because the accelerated particle eventually overtakes and the distance continuously increases.
• First increases, reaches a maximum value and then remains constant: This situation would arise if the accelerated particle and the constant velocity particle reach a terminal point where their velocities become equal. However, the accelerated particle in this question keeps increasing its velocity, so the distance does not stabilize.