Velocity-time graphs

The rate of change of displacement of an object, or the change in the object’s location according to a specific frame of reference with regard to time, can be described as velocity. An object’s velocity is a vector quantity, which means. Velocity varies from speed because it includes both magnitude and direction. An object’s speed does not include direction.

The SI unit of velocity is m/s.

Velocity-Time Graph

The velocity-time graph is particularly significant for learning about the motion of any object since it shows the object’s acceleration. It is simple to detect whether an object is accelerating, decelerating, or not accelerating at all based on the many sorts of velocities, for example, an object may have a constant velocity, ascending velocity, or descending velocity.

CASE 1: No Acceleration

When the upper and lower limits of change in velocity remain constant throughout the motion of an object, the object will have some initial velocity and cannot have zero initial velocity, and the slope of the velocity-time graph generated is constant. The continuous slope indicates that the object’s acceleration has not increased or decreased. As a result, the object in this scenario has no acceleration.

In this case, the x-axis represents the time and the y-axis represents the velocity. The graph is parallel to the x-axis and hence the acceleration is zero. 

CASE 2: Constant Acceleration

When an object’s velocity increases throughout its motion, the ultimate velocity exceeds the starting velocity; but, because the object’s speed is always growing, the initial velocity can also be zero. The slope of the velocity-time graph derived in this scenario is increasing, indicating that the body is accelerating at a constant rate.

In this case, the x-axis represents the time and the y-axis represents the velocity. The graph moves upward in a linear manner with respect to the value of time. Since the object is moving with a constant acceleration, the equations of motion can be used to calculate the different parameters of the object in motion.

CASE 3: Increasing Acceleration

The ultimate velocity will be substantially greater than the starting velocity when the rate of change of velocity increases during the motion. The initial velocity in this scenario can also be zero because the object’s acceleration is growing at some rate per second. In this situation, the slope of the velocity-time graph will be in the form of a curve. The curve in the slope indicates that the body is accelerating or decelerating.

In this case, the x-axis represents the time and the y-axis represents the velocity. The graph is in the form of a curve moving in an upward direction. Acceleration of the object can be calculated by finding out the slope of the graph at any point in the graph.

NOTE: In all the 3 cases mentioned above, if you want to calculate the displacement of the object in motion, it can be easily calculated by finding out the area under the graph.

Importance of Slope

The slope of the line on a velocity-time graph represents the object’s acceleration. As explained previously, a horizontal line has a slope of zero, which means the object’s acceleration is zero. A positive acceleration is represented by an upward sloping line, whereas a negative acceleration is represented by a downward sloping line.

Positive Velocity and Negative Velocity

The velocity will be positive whenever the line is in the positive zone (above the x-axis) of the graph, as it is a velocity-time graph. Similarly, if the line is in the negative zone of the graph (below the x-axis), the velocity will be negative. A positive velocity indicates that the object is travelling in the right direction, whereas a negative velocity indicates that the object is moving backwards.

If the line is in the positive zone of the graph, it means the object is going in the right direction (whether it is sloping up or sloping down). And if the line is in the negative section of the graph, you know an object is travelling in the wrong direction (whether it is sloping up or sloping down). Finally, the object has changed the direction if a line crosses the x-axis from the positive to the negative part of the graph (or vice versa).

Speeding Up and Slowing Down

The magnitude (or numerical value) of the velocity is increasing as it speeds up. For example, an object speeding up from +3 m/s to +9 m/s is said to be speeding up. Similarly, an object moving at a rate of -3 m/s to -9 m/s is speeding rapidly. The magnitude of the velocity (only the numerical value) is growing in each case, indicating that the speed is increasing. 

Given this, if the line on a velocity-time graph changes from near the 0-velocity point to a spot further away from the 0-velocity point, one might conclude that the object is speeding up. That example, if the line moves farther from the x-axis (the zero-velocity point), the object is moving faster. In the opposite case, if the line approaches the x-axis, the object is slowing down.

Conclusion

Anything containing Kinetic energy is in motion, whether it be one-dimensional, two-dimensional, rotating motion, or something else altogether. Kinetic energy is responsible for motion, and it is well known that any object’s motion is caused by some external force; inertia prevents objects from moving or stopping on their own, so some external force is required to provide kinetic energy to the object, and providing energy implies that the object has some velocity. There are various types of velocities that an item in motion might have, and graphically illustrating the characteristic of velocity in relation to time is easier.

Some of the key points in this article are:

• The slope of the graph in Velocity-Time Graph gives acceleration
• The area under the graph in Velocity-Time Graph gives displacement
• The average velocity in the Velocity-Time Graph can be calculated by finding the average of all the weighted velocities in the graph