What is the formula for distance given constant velocity and time?
$d = v \cdot t$
What is the formula for the area of a rectangle?
$A = b \cdot h$
What is the formula for the area of a triangle?
$A = \frac{b \cdot h}{2}$
What is the formula for the area of a trapezoid?
$A = \frac{a+b}{2} \cdot h$
How to estimate the distance traveled from a velocity-time graph using Riemann Sums?
1. Divide the time interval into subintervals. 2. Construct rectangles with widths equal to the subinterval lengths. 3. Determine the height of each rectangle (usually the function value at the left, right, or midpoint of the subinterval). 4. Calculate the area of each rectangle. 5. Sum the areas of all rectangles to approximate the total distance.
How to find the total distance traveled given a piecewise function representing velocity?
1. Graph the piecewise function. 2. Divide the graph into geometric shapes (rectangles, triangles, trapezoids). 3. Calculate the area of each shape. 4. Sum the areas, considering signed areas, to find the total distance.
How to solve for time given accumulation and rate of change?
Use the formula $t = \frac{a}{r}$, where $t$ is time, $a$ is accumulation, and $r$ is the rate of change.
What does the area under a velocity vs. time graph represent?
The area represents the displacement (total distance traveled) of the object.
On a distance vs. time graph, what does a negative area indicate?
A negative area indicates movement in the opposite direction or a decrease in distance from the starting point.
