Question

Deena made a chart to summarize features of a velocity vs. time graph for objects with constant acceleration and objects with constant velocity.

A 2-column table with 2 rows. The first column is labeled constant acceleration with entries the line is diagonal and straight, find displacement by subtracting the area of the triangle from the area of the rectangle under the line, find acceleration by finding the slope of the line. Second column is labeled constant velocity with entries the line is horizontal, find displacement using the area of the rectangle under the line only, find velocity by locating the values plotted on the y-axis.
Which best describes Deena’s error?

The line for constant velocity is not horizontal; it is diagonal and slopes downward.
The area of the rectangle and the triangle under the line should be added together for constant acceleration
Find acceleration by finding the area of the rectangle above the line.
Find velocity by calculating the slope of the line.

Answer 1

The second choice. For constant acceleration the displacement is the total area under the v–t line, which is the rectangle (v0·t) plus the triangle (½·Δv·t) — you add them, not subtract. The other statements are incorrect: a constant-velocity line is horizontal and acceleration is given by the slope.