A graph shows distance on the vertical axis and time on the horizontal axis. If the speed is steadily increasing, and becomes a curved line on the graph, could any part of the speed lone ever become perfectly vertical? Why or why not?
Since slope on the distance time graph is velocity, it is hard to conceive that position changes instaneously.
A vertical line will have a gradient corresponding to a velocity where rise/run=rise/0 which is an infinite velocity. As nothing can move faster than the veloity of light, a vertical (infinite) gradient is impossible.
In order to determine whether any part of the speed line on a distance-time graph can become perfectly vertical, we need to understand the relationship between speed and distance.
The speed of an object is defined as the rate at which it covers a certain distance. Mathematically, it is calculated by dividing the distance traveled by the time taken:
Speed = Distance / Time
On a distance-time graph, speed is represented by the slope of the line. A steeper slope indicates a higher speed, and a gentler slope indicates a lower speed.
Now, let's consider the scenario where the speed line becomes a curved line on the graph due to steadily increasing speed. This implies that the object is accelerating, as its speed is changing over time.
Acceleration is defined as the rate at which an object's velocity (speed in a particular direction) changes. It can be positive (when the object is speeding up) or negative (when the object is slowing down). When an object's speed is increasing, the acceleration is positive.
Since the speed line is becoming curved, it indicates that the object is accelerating and its speed is changing over time. At any instant in time, the speed of the object is represented by the tangent line to the curve. The slope of this tangent line represents the instantaneous speed at that particular moment.
Now, to answer the question, can any part of the speed line become perfectly vertical?
The answer is no. By definition, a perfectly vertical line on a distance-time graph would represent an infinite speed since the distance covered would be zero. In other words, the object would have covered an infinite amount of distance in zero amount of time, which is not physically possible.
Therefore, on a distance-time graph, the speed line can never become perfectly vertical because it would imply an infinite speed, which is not feasible. However, the speed line can approach a vertical line (become very steep) if the object's speed is increasing rapidly over a short period of time.