Read the statements below and answer the questions that follow

MATHEMATICS · Subjective · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives

Problem

Read the statements below and answer the questions that follow. A differentiable function s(t)s(t) represents the position of a particle on a straight track after tt seconds. (i) Explain the meaning of the expression lim⁡Δt→0s(t+Δt)−s(t)Δt\displaystyle\lim_{\Delta t\to0}\frac{s(t+\Delta t)-s(t)}{\Delta t} in the context of motion. (ii) Describe how the average velocity over a short time interval is related to the instantaneous velocity of the particle. (iii) Using the function s(t)=cos⁡t  (metres)s(t)=\cos t\;\text{(metres)}, interpret the sign of the velocity at t=π3t=\tfrac{\pi}{3} and at t=4π3t=\tfrac{4\pi}{3}, stating clearly what positive and negative values indicate about the direction of motion.

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