D

Step 1: Analyze the objects' motion
We have two objects: one sliding down a frictionless inclined plane and the other falling freely.
Step 2: Determine the speed of each object
- For the sliding object on the inclined plane, the speed can be calculated using energy conservation or kinematics, but it will depend on the angle of the incline.
- For the freely falling object, its speed will be given by the equation:
$$ v = gt $$
where $g$ is acceleration due to gravity and $t$ is the time of fall.
Step 3: Analyze the acceleration
- The acceleration of the object on the inclined plane is given by:
$$ a = g imes ext{sin}( heta) $$
- The falling object has an acceleration of:
$$ a = g $$
These accelerations are not the same unless the incline angle $ heta$ is 90 degrees (which would not be an incline).
Step 4: Determine the time taken
The time taken will also differ between the two objects:
- The sliding object’s time is affected by its angle and the distance along the incline.
- The falling object will fall freely for the time calculated with the free fall equation.
Conclusion
Since both objects do not share the same speed, acceleration, or time, the correct answer is option D: None of the above.