Movement & Position

What the area means

• The area enclosed between a velocity-time line and the time axis equals the distance that has been covered during the interval (or, equivalently, the magnitude of the displacement if the motion runs in a single direction)
• This is true because area = velocity × time on every thin vertical strip under the line, and velocity × time = distance moved in that strip

Splitting a multi-stage motion into shapes

• A constant-velocity section is a horizontal line, so the area under it is a rectangle:

rectangle area = base × height

• A section of constant acceleration or deceleration is a straight slope, so the area under it (down to the time axis) is a triangle:

triangle area = ½ × base × height

• A section that combines a non-zero starting velocity with an acceleration gives a trapezium; split it into a rectangle and a triangle and add the two
• The total distance for a multi-stage motion is found by adding together the area of every enclosed region one stage at a time