All Flashcards

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.

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?

$A = \frac{a+b}{2} \cdot h$

Explain how the area under a velocity-time graph relates to distance.

The area under a velocity-time graph represents the total distance traveled.

What does a definite integral calculate?

The exact area under a curve between two specified limits.

Why are Riemann Sums approximations?

Riemann Sums use rectangles to approximate the area, which may not perfectly match the curve, leading to over or underestimations.

How do integrals 'undo' derivatives?

Integration is the reverse process of differentiation; it finds the original function before differentiation.