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>>Motion in a Straight Line
>>Acceleration
>> $The position of a particle is given by r$

Question

The position of a particle is given by $r = 3.0 t \hat{i} - 2.0 t^{2} \hat{j} + 4.0 \hat{k} m$ where t is in seconds and the coefficients have the proper units for $r$ to be in metres(a) Find the $v$ and $a$ of the particle?(b) What is the magnitude and direction of velocity of the particle at t = 2.0 s ?

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Solution

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(a)
$v (t) = d r / d t$
$= 3.0 \hat{i} - 4.0 t \hat{j}$

$a (t) = d v (t) / d t$
$= - 4.0 \hat{j}$

(b)
$v (2) = 3.0 \hat{i} - 8.0 \hat{j}$
$v (2) = 8.54 m / s$
$∠ v (2) = t a n^{- 1} (- 8 / 3) = - 69.4 4^{\circ} w i t h x a x i s$

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