a spacecraft in deep space fires its thruster, which ejects fuel from the spacecraft. the ejected fuel…
a spacecraft in deep space fires its thruster, which ejects fuel from the spacecraft. the ejected fuel exerts a constant force on the spacecraft and the total mass of the spacecraft decreases at a constant rate. which of the following graphs best represents the acceleration of the spacecraft as a function of time while the thruster is firing?
Answer
Explanation:
Step1: Apply Newton's second law
Newton's second law is (F = ma), where (F) is the force, (m) is the mass, and (a) is the acceleration. Given that the force (F) is constant. As the spacecraft ejects fuel, its mass (m) decreases over time. Rearranging the formula for acceleration gives (a=\frac{F}{m}).
Step2: Analyze the relationship between acceleration and mass
Since (F) is constant and (m) is decreasing (because fuel is being ejected at a constant rate), the acceleration (a) is inversely proportional to the mass (m). As time increases, (m) gets smaller, so (a) gets larger. The rate of change of mass is constant (fuel is ejected at a constant rate). The initial mass is larger, so the initial acceleration is smaller. As time goes on, the decrease in mass leads to a non - linear increase in acceleration. The curve should start with a relatively small slope (initial low acceleration) and then the slope of the (a - t) curve (since (a) is on the y - axis and (t) is on the x - axis) should increase.
Answer:
B