Mechanics

Newton's laws will govern the movement of human powered vehicles. Quantities such as their position, speed, and acceleration will be important in evaluating their performance. The diagram opposite represents how these quantities might behave as a function of time for a vehicle moving in a straight line. To keep things simple, the vehicle will be thought of as a point mass, m.

Curve (a) shows the position of the mass as a function of time. The slope, (Ds/Dt), at any given time gives the average velocity over the time interval Dt. The velocity is defined as the value of this slope in the limit of the time interval going to zero: v = (ds/dt).

Plotting the velocity from (a) as a function of time gives the (b) curve. The slope of this curve at any given time is the acceleration of the mass at that time: a = (dv/dt) = (d²s/dt²). The area under the velocity time curve is the total distance travelled: (s₂ - s₁)

Curve (c) is a plot of the acceleration as a function of time. The area under this curve between t₁ and t₂ is the change in velocity over this time period: (v₂ - v₁)

From: Meriam, "Dynamics," Wiley (1975)