ABSTRACT
Recall the example from Chapter 2 in which the explicit form of the trajectory of a particle was quoted: x(t) = b t3, for b, a constant.
Q: How did we know this?
A: Perhaps it had been ascertained that the acceleration of the particle increased linearly with time. A felicitous choice of time parameterisation enabled a single simple expression to describe the acceleration in a manner consistent with the initial data:
a(t) = 6 b t , and v0 = v(t) ∣∣∣ t=0
= 0 , x0 = x(t) ∣∣∣ t=0
= 0 .
