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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 1 s and 2 s is:
Explanation
We have given, $v = \alpha t + \beta t^{2}$ $\Rightarrow ds/dt = \alpha t + \beta t^{2}$ $\Rightarrow \int_{s_{1}}^{s_{2}}{ds = \int_{1}^{2}{(\alpha t + \beta t^{2})dt}}$ $\Rightarrow s_{2} - s_{1} = \left[ \frac{\alpha t^{2}}{2} + \frac{\beta t^{3}}{3} \right]_{1}^{2}$ As particle is moving in a straight line, $\therefore$ Distance = Displacement