Velocity of an object in rectilinear motion i | vedclass

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Question

(A) The average velocity $v_{avg}$ is defined as the total displacement divided by the total time interval.
$v_{avg} = \frac{\Delta x}{\Delta t} = \f

Vedclass · Accepted Answer

$-1$

Vedclass · Answer

(A) The average velocity $v_{avg}$ is defined as the total displacement divided by the total time interval.
$v_{avg} = \frac{\Delta x}{\Delta t} = \frac{1}{t_2 - t_1} \int_{t_1}^{t_2} v(t) \, dt$
Given $v(t) = t - t^3$,$t_1 = 0 \ s$,and $t_2 = 2 \ s$.
$v_{avg} = \frac{1}{2 - 0} \int_{0}^{2} (t - t^3) \, dt$
$v_{avg} = \frac{1}{2} \left[ \frac{t^2}{2} - \frac{t^4}{4} \right]_{0}^{2}$
$v_{avg} = \frac{1}{2} \left[ (\frac{2^2}{2} - \frac{2^4}{4}) - (0 - 0) \right]$
$v_{avg} = \frac{1}{2} \left[ (\frac{4}{2} - \frac{16}{4}) \right]$
$v_{avg} = \frac{1}{2} [2 - 4] = \frac{1}{2} [-2] = -1 \ m/s$.
Note: Since the result is $-1 \ m/s$ and it is not among the options,the question or options may be flawed. However,based on the calculation,the value is $-1$.

Velocity of an object in rectilinear motion is given as a function of time by $v = t - t^3$,where $v$ is in $m/s$ and $t$ is in seconds. Its average velocity over the time interval from $t = 0 \ s$ to $t = 2 \ s$ is ........ $m/s$.

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