Velocity

A particle mo...

Question

A particle moves in a straight line. Its position (in $m$ ) as function of time is given by
$x = ({a t}^{2} + b)$
What is the average velocity in time interval $t = 3 s$ to $t = 5 s$ in ${m s}^{- 1}$ . (Where $a$ and $b$ are constants and $a = 1 {m s}^{- 2}$ , $b = 1 m$ )

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Solution

$a = 1 m s^{- 2} b = 1 m$
$x (t) = t^{2} + 1$
$x (3) = 9 + 1 = 10 m$
$x (5) = 25 + 1 = 26 m$
$v_{a v g}$ from t = 3s to t = 5s $= \frac{x (5) - x (3)}{2}$
$v_{a v g} = \frac{26 - 10}{2} = 8 m / s$

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