As v goes up what happens to ac? The image contains a question and four graphs. The question asks: "Which graph best represents the relationship between the magnitude of the centripetal acceleration and the speed of an object moving in a circle of constant radius?"There are four graphs labeled (1) to (4), each illustrating a different relationship between centripetal acceleration (on the y-axis) and speed (on the x-axis):1. **Graph (1):** Shows a linear increase in centripetal acceleration with speed, represented by a straight line starting from the origin and moving upwards to the right.2. **Graph (2):** Displays an exponential growth curve where centripetal acceleration increases rapidly as speed increases, forming a curve that gets steeper.3. **Graph (3):** Represents a downward curve, suggesting a decreasing relationship, where centripetal acceleration decreases as speed increases.4. **Graph (4):** Shows centripetal acceleration as a constant value regardless of speed, represented by a horizontal line.The question requires selecting the graph that properly illustrates the mathematical relationship between centripetal acceleration and speed. In physics, centripetal acceleration is proportional to the square of the speed (a = v²/r), indicating that the relationship is parabolic, similar to Graph (2).

Given data: Object moving in circular path Radius is constant Required: Relationship between centripetal acceleration and speed of the objectThe motion of the object The centripetal acceleration is given by ac = v2/r Here, v = speed of the object r = radius of the circular path Given that, the radius of the circular path is constant. So the centripetal acceleration is directly proportional to square of the speed of the object. The graph between centripetal acceleration and speed of the object Hence, the correct answer is option (2)