For a particle

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

For a particle, the displacement as a function of time is

x(t)=6t-0.5t^{2}

(SI units). (a) Determine the average velocity in the interval

t=0

t=6\,\text{s}

. (b) Find the instantaneous velocity at

t=3\,\text{s}

and comment on its relation to the value obtained in part (a).

Related theory

Differentiation Rules
Derivative Foundations
Differentiation from first principles
Intuitive idea of derivatives
Limits and Derivatives

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