Question

Suppose the initial position of an object is zero, the starting velocity is 3 m/s and the final velocity was 10 m/s. The object moves with constant acceleration. Which part of a velocity vs. time graph can be used to calculate the displacement of the object?

the area of the rectangle under the line
the area of the rectangle above the line
the area of the rectangle plus the area of the triangle under the line
the area of the rectangle plus the area of the triangle above the line

Answer 1

The area of the rectangle plus the area of the triangle under the line.

Reason: displacement = area under the v(t) curve down to the time axis. With v changing from 3 to 10 m/s in time t that area = rectangle (height 3, area 3t) plus triangle (base t, height 10−3, area 0.5·(10−3)·t). So
displacement = 3t + 0.5·7t = (3+10)/2 · t = 6.5 t.