"The instantaneous velocity of a particle moving in a straight line is given as $V = \alpha t + \beta {t^2}$, where $\alpha$ and $\beta$ are constants. The distance travelled by the particle between 1s and 2s is :"

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"$V = \alpha t + \beta {t^2}$

${{ds} \over {dt}} = \alpha t + \beta {t^2}$

$\int\limits_{{S_1}}^{{S_2}} {ds = \int\limits_1^2 {(\alpha t + \beta {t^2})dt} }$

$${S_2} - {S_1} = \left[ {{{\alpha {t^2}} \over 2} + {{\beta {t^3}} \over 3}} \right]_1^2$$

As particle is not changing direction

So distance = displacement

Distance = $\left[ {{{\alpha [4 - 1]} \over 2} + {{\beta [8 - 1]} \over 3}} \right]$

$= {{3\alpha } \over 2} + {{7\beta } \over 3}$"

The instantaneous velocity of a particle moving in a straight line is given as $V = \alpha t + \beta {t^2}$, where $\alpha$ and $\beta$ are constants. The distance travelled by the particle between 1s and 2s is :

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The instantaneous velocity of a particle moving in a straight line is given as $V = \alpha t + \beta {t^2}$, where $\alpha$ and $\beta$ are constants. The distance travelled by the particle between 1s and 2s is :

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