Final Answer:
The deflection (displacement) of the car when the train is at rest (x1=0) for k=1 N/m is 0 meters. The velocity of the car when the train is at rest (x1=0) for k=1 N/m is 0 m/s. The acceleration of the car when the train is at rest (x1=0) for k=1 N/m is 0 m/s².
Step-by-step explanation:
The deflection or displacement of the car when the train is at rest (x1=0) for k=1 N/m is determined by Hooke's Law, which states that the displacement (x) is directly proportional to the force applied (F) and inversely proportional to the spring constant (k). Mathematically, it's represented as x = F / k. Here, for k=1 N/m and considering the train at rest (x1=0), the displacement of the car (x) is 0 meters since the force applied is 0, resulting in no displacement.
Regarding the velocity of the car, when the train is at rest (x1=0) for k=1 N/m, it remains stationary. Velocity is the rate of change of displacement over time (v = dx/dt). As there's no displacement (x=0) occurring due to the train being at rest, the velocity (v) of the car is 0 m/s, implying no movement or change in position.
Lastly, the acceleration of the car when the train is at rest (x1=0) for k=1 N/m is also 0 m/s². Acceleration is the rate of change of velocity over time (a = dv/dt). Since the velocity remains constant at 0 m/s due to the stationary nature of the car when the train is at rest, there is no change in velocity, resulting in an acceleration of 0 m/s².
Therefore, in summary, the car experiences no deflection or displacement, maintains a constant velocity of 0 m/s, and undergoes zero acceleration when the train is at rest (x1=0) for k=1 N/m.