For a velocity-time graph, what does the "tangent line of the curve" represent?
math.sc.edu/~diestelg/teaching/calcnotes.pdf
the tangent line of the curve s(t) = t. 2 +2t at the point (1, s(1)) = (1, 3) ... 0, y = 0 or y = 3. Therefore, the graph does not pass the. vertical line test.
If velocity is on your vertical axis and time is on your horizontal axis, then the slope at a point on the curve is the slope of the tangent to the curve at that point.
That is the (change in velocity)/(change in time) at that point on the curve, which is the ACCELERATION at that time.
The tangent line of the curve on a velocity-time graph represents the instantaneous velocity of an object at a specific point in time. To find the tangent line, follow these steps:
1. Locate the point on the graph where you want to find the instantaneous velocity.
2. Draw a straight line that touches the curve at that point without crossing it. This line is the tangent line.
3. Determine the slope of the tangent line. The slope represents the rate of change of velocity at that specific time.
4. The magnitude and sign of the slope will indicate whether the object is speeding up, slowing down, or maintaining a constant velocity at that instant in time.
In summary, the tangent line of the curve on a velocity-time graph provides information about the instantaneous velocity of an object at a specific point in time.