A particle moves along a straight line so that its displacement after seconds is…

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

A particle moves along a straight line so that its displacement after tt seconds is given by s(t)=2t3s(t)=2t^{3} metres. (i) Obtain an expression for its instantaneous velocity at time tt by evaluating lim⁡h→0s(t+h)−s(t)h\displaystyle \lim_{h\to 0}\dfrac{s(t+h)-s(t)}{h}. (ii) Find the velocity of the particle at t=3 st=3\,\text{s}. (iii) Differentiate 2t32t^{3} by the standard rule and confirm that the result agrees with part (i).

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