Final answer:
The velocity of the model rocket increases linearly with time under constant acceleration, while its displacement increases quadratically.
Kinetic energy changes as the velocity changes and does not remain constant. The decreasing mass of the rocket due to fuel consumption leads to increasing acceleration over time.
The correct option is: b) Its acceleration decreases linearly with time.
Explanation:
The student's question pertains to the motion of a model rocket that is launched upwards with constant acceleration until it runs out of fuel. Using kinematic principles, we can address each statement:
- a) If the acceleration is constant (a), then the velocity (v) increases linearly with time (t), because v = at when the initial velocity is zero.
- b) Since the acceleration is constant, it does not decrease linearly with time. The given statement is incorrect.
- c) The displacement (s) increases quadratically with time when acceleration is constant, as represented by the equation s = (1/2)at².
- d) The kinetic energy (KE) of the rocket changes as its velocity changes because KE = (1/2)mv² where m is mass and v is velocity. Hence, this statement is incorrect; kinetic energy does not remain constant if the velocity is changing.
When considering the effect of the decreasing mass of a rocket, as fuel is consumed, the acceleration will actually increase because the force (thrust) remains the same while the mass decreases. The total change in the rocket's velocity is thus affected by the rate of fuel consumption, leading to increasing acceleration as mass decreases.