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

The velocity $$(v)-$$ time $$(t)$$ plot of the motion of a body is shown below:

The acceleration $$(a)-$$ time $$(t)$$ graph that best suits this motion is :

The position of a particle is given by

$$\vec{r}(t)=4 t \hat{i}+2 t^2 \hat{j}+5 \hat{k} $$

where $$\mathrm{t}$$ is in seconds and $$\mathrm{r}$$ in metre. Find the magnitude and direction of velocity $$v(t)$$, at $$t=1 \mathrm{~s}$$, with respect to $$\mathrm{x}$$-axis

A vehicle travels half the distance with speed $$v$$ and the remaining distance with speed $$2 v$$. Its average speed is :