Question

In the xy-plane, a particle moves along the parabola y=x² −x. What can be inferred about the motion of the particle?

a) The particle moves along a straight line
b) The particle undergoes circular motion
c) The particle follows a parabolic path
d) The particle remains at a fixed position

Answer 1

The motion of the particle moving along the parabola y=x² − x is parabolic. The correct answer is c) The particle follows a parabolic path, which implies acceleration in its movement.

Step-by-step explanation:

The motion of a particle moving along the parabola y=x² − x in the xy-plane can be inferred based on the equation of the path it follows. Since the equation is quadratic in form, which describes a parabola, it can be concluded that the particle follows a parabolic path. Therefore, the correct answer to the question is c) The particle follows a parabolic path. The path through space-time of a particle is called the world line of the particle. Unlike a straight line which suggests constant velocity, or a circle suggesting uniform circular motion, the parabolic nature implies that the particle is accelerating as it moves along the xy-plane. Considering real-world scenarios, such as a projectile motion under gravity, the path followed can be similarly parabolic.