Velocity represents the slope of a displacement function. Suppose an object was moving to the right, then stopped, then continued moving to the right. What would the displacement function look like?
increasing, constant, then increasing
(assuming that "to the right" is in the positive direction)
To understand what the displacement function would look like, let's break down the scenario step by step:
1. Object moving to the right: In this phase, the object is steadily moving in one direction. The displacement function during this time would be a linear function, because the object is moving with constant velocity. The slope of the displacement function would represent the velocity of the object.
2. Object stops: At some point, the object stops. This means that its velocity becomes zero. When the object is stationary, the slope of the displacement function would also be zero. Thus, during the time when the object is not moving, the displacement function would be a horizontal line, indicating no change in position.
3. Object continues moving to the right: After the object stops, it starts moving again in the original direction. The same linear function representing the initial motion would continue, but with a different starting point, as the object has already covered some distance during the first phase.
Overall, the displacement function would be a combination of a linear function for the initial motion, followed by a horizontal line during the stationary phase, and then again continuing as a linear function for the subsequent motion.