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A particle moves in a plane with a constant acceleration in a direction different from the initial velocity. The path of the particle is
- a)A straight line
- b)An arc of circle
- c)A parabola
- d)An ellipse
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A particle moves in a plane with a constant acceleration in a directio...
Explanation:
The motion of the particle in a plane with a constant acceleration in a direction different from the initial velocity is a two-dimensional motion. The path of the particle depends on the direction of the acceleration with respect to the initial velocity.
The path of the particle is a parabola because the acceleration acts perpendicular to the initial velocity. This means that the particle will move along a curved path that is determined by the combination of the initial velocity and the acceleration.
The motion of the particle can be analyzed using the equations of motion for two-dimensional motion:
x = x0 + v0x t + 1/2 ax t^2
y = y0 + v0y t + 1/2 ay t^2
where x and y are the position coordinates of the particle at time t, x0 and y0 are the initial position coordinates, v0x and v0y are the initial velocity components, ax and ay are the acceleration components.
The equations above show that the path of the particle is a parabola because the position coordinates are proportional to the square of the time. The direction of the curvature of the parabola depends on the sign of the acceleration components.
Conclusion:
Therefore, the correct answer is option 'C' which says that the path of the particle is a parabola.
The motion of the particle in a plane with a constant acceleration in a direction different from the initial velocity is a two-dimensional motion. The path of the particle depends on the direction of the acceleration with respect to the initial velocity.
The path of the particle is a parabola because the acceleration acts perpendicular to the initial velocity. This means that the particle will move along a curved path that is determined by the combination of the initial velocity and the acceleration.
The motion of the particle can be analyzed using the equations of motion for two-dimensional motion:
x = x0 + v0x t + 1/2 ax t^2
y = y0 + v0y t + 1/2 ay t^2
where x and y are the position coordinates of the particle at time t, x0 and y0 are the initial position coordinates, v0x and v0y are the initial velocity components, ax and ay are the acceleration components.
The equations above show that the path of the particle is a parabola because the position coordinates are proportional to the square of the time. The direction of the curvature of the parabola depends on the sign of the acceleration components.
Conclusion:
Therefore, the correct answer is option 'C' which says that the path of the particle is a parabola.
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A particle moves in a plane with a constant acceleration in a direction different from the initial velocity. The path of the particle isa)A straight lineb)An arc of circlec)A parabolad)An ellipseCorrect answer is option 'C'. Can you explain this answer?
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