The position of a particle moving on the x-axis is given by $x = 7.8 + 9.2 t - 2.1 t^{3}$ with x in meters and t in seconds. What is its velocity at t = 3.5 s? Is the velocity constant, or is it continuously changing?

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Solution

To measure instantaneous velocity we have to differentiate the position function with respect to time.
$v = \frac{d x}{d t} = \frac{d}{d t} (7.8 + 9.2 t - 2.1 t^{3})$
$v = 9.2 - 9.3 t^{2}$
At $t = 3.5 s$ we get,
$v = 9.2 - 6.3 (3.5)^{2}$
$v = - 67.98 m / s$
As the velocity is given by, $v = 9.2 - 9.3 t^{2}$ which depends on the time $t$ , therefore the velocity is not constant i.e.; continuously changing.

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