Mathematics

Problem

The velocity of a particle is given by

v(t)=3 t^{2}-2 t+4

(in

\text{m s}^{-1}

). Calculate the instantaneous acceleration at

t = 2\,\text{s}

. a)

14\,\text{m s}^{-2}

10\,\text{m s}^{-2}

12\,\text{m s}^{-2}

8\,\text{m s}^{-2}

Intuitive explanation

Acceleration is the rate of change of velocity—just as velocity measures how position changes, acceleration measures how velocity changes. Since you're given $v(t)$ as a function of time, take its derivative with respect to $t$ to get the acceleration function $a(t)$ , then evaluate it at the specific moment $t = 2\,\text{s}$ .

Intuitive explanation

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