A particle is moving along $x$-axis with its position $(x)$ varying with time $(t)$ as $x=\alpha x^4

Question

A particle is moving along $x$-axis with its position $(x)$ varying with time $(t)$ as $x=\alpha x^4+\beta t^2+\gamma t+\delta$. The ratio of its initial acceleration, respectively, is

Professor PC Thomas Classes · Answer

(d) : Given, position, $(x)=\alpha t^4+\beta t^2+\gamma t+\delta$ Velocity, $(v)=\frac{d x}{d t}=4 \alpha t^2+2 \beta t+\gamma$ Initial velocity, $
u($ at $t=0)=\gamma$ Acceleration, $(a)=\frac{d v}{d t}=12 \alpha t^2+2 \beta$ Initial acceleration, $a$ (at $t=0$ ) $=2 \beta$ From equation (i) and (ii) $ \frac{v(0)}{a(0)}=\frac{\gamma}{2 \beta}=\gamma: 2 \beta $