A particle enters motion at time t = 0 (time plotted on x-axis) until sometime t = n > 0. S ⊆ R \times R is a relation where the pair (t, p) in S relates the time t to the position of the particle p at that time. Is S a function, or equivalently is p(t) a function of t? If so, show that it satisfies the properties of a function. What is its domain and image? What should be the motion of this particle be such that p is injective?