Can you teach me how to find the displacement and distance from a v vs t graphs area. For example like the question should have a graph that starts at -12m/s and goes to 48m/s in 50s.---Chart Description:
* Type: Line chart.
* Title: velocity east vs. time.
* X-axis:
* Label: time (s)
* Scale: Ranges from 0 to 50, with major ticks at 10, 20, 30, 40, 50. The grid lines are spaced every 1 unit.
* Y-axis:
* Label: velocity east (m/s)
* Scale: Ranges from -20 to 60, with major ticks at -20, -10, 0, 10, 20, 30, 40, 50, 60. The grid lines are spaced every 2 units.
* Data Series: A single blue straight line.
* The line starts near (0, -12).
* The line passes through (10, -2).
* The line passes through (20, 8).
* The line passes through (30, 18).
* The line passes through (40, 28).
* The line passes through (50, 38).
* The line extends from the left edge of the graph (at time = 0) to the right edge (at time = 50).
* The line represents a positive slope, indicating that the velocity east is increasing linearly with time.
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Welcome! Today we'll learn how to find displacement and distance from velocity-time graphs using the area under the curve. The key concept is that the area under a v-t graph represents motion quantities. For displacement, we use the signed area where regions above the time axis are positive and below are negative. For distance, we use the total absolute area. Let's examine a specific example where velocity changes linearly from negative twelve meters per second to positive thirty-eight meters per second over fifty seconds.
Now let's find the equation of this velocity line. We have two points: zero seconds at negative twelve meters per second, and fifty seconds at thirty-eight meters per second. To find the slope, we calculate the change in velocity divided by the change in time. That's thirty-eight minus negative twelve, which equals fifty, divided by fifty minus zero, which also equals fifty. So our slope is one meter per second squared. Since the line passes through zero seconds at negative twelve meters per second, our equation is v of t equals t minus twelve.