VT Graphs

An object’s velocity is its speed in a given direction. Two automobiles travelling at the same speed but in separate directions have velocities that vary.

A velocity-time graph illustrates the speed and direction of an item over a specified time period. Velocity-time graphs are sometimes referred to as speed-time graphs in some circles.

The vertical axis of a velocity-time graph represents the object’s velocity. The horizontal axis displays the amount of time that has passed since the beginning.

Positive velocity vs. negative velocity

A positive velocity would be observed whenever the line crosses the positive section (i.e., above the x-axis) of the graph, which is the case because the graph is a velocity-time graph. Similarly, whenever the line is in the negative zone (below the x-axis) of the graph, the velocity will be negative as well. A positive velocity indicates that the item is travelling in the positive direction, whilst a negative velocity indicates that the object is going in the negative direction (or vice versa). As a result, if the line is placed in the positive section of the graph, it indicates that the item is travelling in the positive direction (whether it is sloping up or sloping down). Furthermore, if the line is positioned in the negative area of the graph, it is known that an object is travelling in the negative direction of the graph (whether it is sloping up or sloping down). Finally, if a line crosses over the x-axis from the positive portion of the graph to the negative section of the graph (or vice versa), the item has shifted its orientation.

Identifying the velocity vector’s direction

Defining the direction of the velocity vector is straightforward. The direction of the velocity vector is identical to the direction of motion of an item. It makes no difference whether the item is accelerating or decelerating. If an item is travelling to the right, its velocity is said to be rightward. If an item is going downhill, it is said to have a downward velocity. Thus, an aeroplane travelling west at a speed of 300 miles per hour has a westward velocity of 300 miles per hour. It is worth noting that speed has no direction (it is a scalar), but velocity at every time is just the speed number with a direction.

Representation of vertical axis on a velocity graph

The vertical axis denotes the object’s velocity. While this may seem self-evident, be warned velocity graphs are notoriously difficult to understand. People become so accustomed to judging velocity by the slope, as they would with a position graph, that they forget that with velocity graphs, the value on the vertical axis represents the velocity.

Representation of slope of a velocity graph

The slope of a velocity graph indicates the object’s acceleration. Thus, the slope value at a specific moment indicates the object’s acceleration at that instant.

The Importance of Slope

The geometries of the velocity vs. time graphs for these two fundamental types of motion – constant velocity and accelerated motion (i.e., changing velocity) – indicate a critical concept. The premise is that the slope of a velocity-time graph contains important information about the object’s acceleration. If the acceleration is equal to zero, the slope is also equal to zero (i.e., a horizontal line). If the acceleration is more than zero, the slope is greater than zero (i.e., an upward sloping line). Negative acceleration results in a negative slope (i.e., a downward sloping line). This is a general principle that may be applied to every possible motion.

Conclusion

A velocity time graph is a visual depiction of the velocity of any moving object as a function of time. This graph may take on any shape. When motion is accelerated or slowed, the line in the vt graph is not parallel to either axis.