Mathematics

Mathematics

Problem

A particle moves along a straight line, and its position at time tt seconds is described by s(t)s(t). Which of the following expressions represents the particle’s instantaneous velocity v(t)v(t)? a) s(t+Δt)−s(t)Δt\displaystyle \frac{s(t+\Delta t)-s(t)}{\Delta t} for a fixed non-zero Δt\Delta t b) s(t)−s(0)t\displaystyle \frac{s(t)-s(0)}{t} c) s′(t)s'(t) d) s(t+Δt)−s(t−Δt)2 Δt\displaystyle \frac{s(t+\Delta t)-s(t-\Delta t)}{2\,\Delta t} for a fixed non-zero Δt\Delta t

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