Given: The initial position of the block is the origin; i.e., x = 0 at t = 0 . Consider down the track to be the positive x-direction. A block with an initial velocity v0 slides up and back down a frictionless incline. Which graph best represents a description of the velocity of the block versus time?
To determine the graph that best represents the velocity of the block versus time, we need to consider the motion of the block while sliding up and back down the incline.
When the block is sliding up the incline, its velocity will decrease since it is moving against the gravitational force. This means the velocity is negative (opposite to the positive x-direction). As the block reaches its highest point and starts sliding back down, its velocity will increase in the positive x-direction, as it is now moving with the force of gravity.
Based on this information, the graph should show a negative velocity while the block is moving up the incline and a positive velocity while the block is moving back down.
Therefore, the correct graph would show a declining curve (negative slope) as the block moves upwards, reaching a minimum value at the highest point, and then showing an increasing curve (positive slope) as the block descends back down.
The graph that best represents this description is a concave-down curve (like a bowl shape) showing a decreasing velocity while the block moves upwards and an increasing velocity as it moves downwards.