Question #7ea57

Oct 29, 2016

$2 {a}_{2}$

Explanation:

Given that displacement $x$ of a particle moving along a straight line at time $t$ is given by the equation
$x = {a}_{0} + {a}_{1} t + {a}_{2} {t}^{2}$
where ${a}_{0} , {a}_{1} \mathmr{and} {a}_{2}$ are constants
We know that velocity $v$ is given by rate of change of displacement
$\therefore v = \frac{\mathrm{dx}}{\mathrm{dt}} = \frac{d}{\mathrm{dt}} \left({a}_{0} + {a}_{1} t + {a}_{2} {t}^{2}\right)$
$\implies \frac{\mathrm{dx}}{\mathrm{dt}} = {a}_{1} + {a}_{2} \times 2 \times t$
$\implies \frac{\mathrm{dx}}{\mathrm{dt}} = {a}_{1} + 2 {a}_{2} t$

We also know that acceleration $a$ is given by rate of change of velocity
$\therefore a = \frac{\mathrm{dv}}{\mathrm{dt}} = \frac{d}{\mathrm{dt}} \left({a}_{1} + 2 {a}_{2} t\right)$
$\therefore a = \frac{\mathrm{dv}}{\mathrm{dt}} = 2 {a}_{2}$