There is a parabolic position vs time graph.
Which of these is true:
The object moves
1. in a parabolic trajectory.
2. along a straight line.
3. along an arc of a circle
wouldn't 1 and 3 produce the same/similar position graph?
No, #1 and #3 would be different trajectories. Note that they are asking about position vs. time, not about the shape of the trajectory
So in which one would the graph of position vs time be a parabola?
If the object moves along a straight line, then wouldn't the position graph just be an increasing line with with positive slope?
If position vs time is a parabolca, the object is accelerating at a constant rate along a straight line.
To determine the correct statement, let's understand the motion associated with each option:
1. Parabolic trajectory: If the object moves in a parabolic trajectory, its position vs. time graph will resemble a parabolic curve. This means that the object experiences a smooth, curved path like a projectile in free fall or a ball thrown through the air.
2. Straight line: If the object moves along a straight line, its position vs. time graph will be a straight line. This indicates that the object maintains a constant velocity, covering equal distances in equal intervals of time.
3. Arc of a circle: If the object moves along an arc of a circle, its position vs. time graph will deviate from both options 1 and 2. It would resemble part of a circular curve, suggesting that the object is undergoing circular motion.
Now, considering options 1 and 3, they would indeed produce similar position graphs, both representing curved trajectories. However, there is a subtle difference:
- Option 1 denotes motion along a parabolic trajectory, which implies the object moves freely under the influence of gravity or other similar forces.
- Option 3 suggests motion along an arc of a circle, which implies the object is under the effect of a centripetal force, causing it to rotate around a fixed point.
Thus, if the position vs. time graph exhibits a parabolic curve, option 1 would be correct, indicating a parabolic trajectory. Option 3 would be incorrect as it represents circular motion.