If the stationary object were to accelerate towards the ship at a rate of 10 m/sec^2, the relative velocity between the ship and the object would change over time. Initially, the ship is moving away from the object at a constant velocity of 100 m/sec. However, as the object accelerates towards the ship, its velocity relative to the ship will increase.
To analyze this scenario, let's break it down into two phases:
Phase 1: Initial motion In this phase, the ship is moving away from the stationary object at a constant velocity of 100 m/sec. As a result, the relative velocity between the ship and the object is also 100 m/sec in the opposite direction.
Phase 2: Object acceleration During this phase, the object accelerates towards the ship at a rate of 10 m/sec^2. The ship's velocity remains constant at 100 m/sec. However, the object's velocity increases over time due to the acceleration. The relative velocity between the ship and the object will be the difference between their velocities at any given moment.
To determine the relative velocity during phase 2, we need to use the equations of motion. Let's assume that the object starts from rest relative to the ship at the beginning of phase 2. We can use the following equation:
v_object = u_object + a_object * t
Where:
- v_object is the velocity of the object relative to the ship,
- u_object is the initial velocity of the object relative to the ship (0 m/sec since it starts from rest),
- a_object is the acceleration of the object relative to the ship (10 m/sec^2),
- t is the time elapsed since the beginning of phase 2.
Since the ship's velocity remains constant at 100 m/sec during this phase, the relative velocity can be calculated as:
relative velocity = 100 m/sec - v_object
As time passes, the object's velocity will increase according to the equation above, and the relative velocity between the ship and the object will decrease.
Note that if the ship were to observe the object's motion from its own reference frame, the object's acceleration would not affect the observed relative velocity. The ship would still observe the object moving away at a constant velocity of 100 m/sec, regardless of the object's acceleration. The acceleration only affects the relative velocity when observed from the reference frame of the ship.