The slope of a velocity vs. time graph represents acceleration, calculated as the change in velocity divided by the change in time. A straight line indicates constant acceleration, while the area under the graph represents the displacement.
Relationship Between Slope and a Velocity-Time Graph
The relationship between the slope of a velocity vs. time graph and acceleration is fundamental in understanding motion. The slope is calculated as the rise divided by the run. On a velocity-time graph, 'rise' represents the change in velocity (Δv), and 'run' represents the change in time (Δt). Therefore, the slope (Δv/Δt) corresponds to the acceleration of an object.
For uniform acceleration, the graph is a straight line, indicating a constant slope and hence constant acceleration. If the graph curves upward, it suggests that the acceleration is increasing, while if it curves downward, the acceleration is decreasing. The area under the velocity-time graph indicates the displacement of the object during the given time interval.
Example: A car accelerating from rest will have a velocity-time graph that starts at the origin and slopes upward. The steeper the slope, the greater the car's acceleration. If the car maintains a constant speed, the slope will be zero, indicating no acceleration.