The slope of the tangent on a position time graph equals what?
speed.
The slope of the tangent on a position-time graph represents the instantaneous velocity of an object at a particular moment in time.
To find the slope of the tangent on a position-time graph, you can follow these steps:
Step 1: Understand the position-time graph. Make sure you have a clear understanding of what the graph represents. The position is shown on the y-axis, representing how far an object is from its starting point, while time is shown on the x-axis, representing the elapsed time.
Step 2: Identify the point on the graph where you want to find the slope of the tangent. Look for a specific point on the curve where you want to determine the slope of the tangent line.
Step 3: Choose two points close to the desired point. Identify two points on the curve that are close to the point where you want to find the tangent. It is helpful to choose points that lie on different sides of the desired point.
Step 4: Determine the change in position and the change in time. Calculate the difference in position (y-values) and the difference in time (x-values) between the two points you selected. This will give you the rise and run values needed to calculate the slope.
Step 5: Calculate the slope. Divide the change in position (rise) by the change in time (run) to calculate the slope. This can be done using the formula: slope = rise / run.
Step 6: Interpret the slope. The value of the slope represents the rate of change of position with respect to time. It indicates how the position is changing over time at the specific point where the tangent is taken. A positive slope indicates an increasing position, a negative slope indicates a decreasing position, and a slope of zero indicates a constant position.
By following these steps, you should be able to find the slope of the tangent on a position-time graph.