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# The figure on the left above shows a wheel with a mark on its rim. The wheel is rolling on the ground at a constant rate along a level straight path from a starting point to an ending point. The graph of *y= d(t)* on the right could represent which of the following as a function of time from when the wheel began to roll?

- The speed at which the wheel is rolling
- The distance of the wheel from its starting point
- The distance of the mark on the rim from the center of the wheel
- The distance of the mark on the rim from the ground

## The correct answer is: The distance of the mark on the rim from the ground

### Solution:-

- First we will analyse the given graph.
- The graph on the right shows the change in distance from the ground of the mark on the rim over time.
- The
*y*-intercept of the graph corresponds to the mark’s position at the start of the motion (*t *= 0); at this moment, the mark is at its highest point from the ground.
- As the wheel rolls, the mark approaches the ground, its distance from the ground decreasing until it reaches 0—the point where it touches the ground.
- After that, the mark moves up and away from the ground, its distance from the ground increasing until it reaches its maximum height from the ground.
- This is the moment when the wheel has completed a full rotation. The remaining part of the graph shows the distance of the mark from the ground during the second rotation of the wheel.
- Therefore, of the given choices, only choice D satisfies with the given information.
- Option A is incorrect because the speed at which the wheel is rolling does not change over time, meaning the graph representing the speed would be a horizontal line.
- Option B is incorrect because the distance of the wheel from its starting point to its ending point increases continuously; the graph shows a quantity that changes periodically over time, alternately decreasing and increasing.
- Option C is incorrect because the distance of the mark from the center of the wheel is constant and equals the radius of the wheel. The graph representing this distance would be a horizontal line, not the curved line of the graph shown.

Therefore the correct option is option D) The distance of the mark on the rim from the ground

*y*-intercept of the graph corresponds to the mark’s position at the start of the motion (*t*= 0); at this moment, the mark is at its highest point from the ground.### Related Questions to study

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