The velocity of a particle is v = v₀ + gt + Ft². Its position is x = 0 at t = 0; then its displacement after time (t = 1) is :

<p>The velocity of a particle is given by $ v = v_0 + gt + Ft^2 $. Its position is $ x = 0 $ at $ t = 0 $. To find its displacement after time $ t = 1 $, follow these steps:</p> <p>Given:</p> <p>$ v = v_0 + gt + Ft^2 $</p> <p>We know that:</p> <p>$ \frac{dx}{dt} = v_0 + gt + Ft^2 $</p> <p>To find the displacement, integrate both sides with respect to $ t $:</p> <p>$ \int_{x = 0}^{x} dx = \int_{t = 0}^{t = 1} (v_0 + gt + Ft^2) \, dt $</p> <p>This simplifies to:</p> <p>$ x = \left[ v_0 t + \frac{gt^2}{2} + \frac{Ft^3}{3} \right]_{t = 0}^{t = 1} $</p> <p>Evaluating the integral from $ t = 0 $ to $ t = 1 $:</p> <p>$ x = v_0 + \frac{g}{2} + \frac{F}{3} $</p> <p>Therefore, the displacement after time $ t = 1 $ is:</p> <p>$ x = v_0 + \frac{g}{2} + \frac{F}{3} $</p>