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 :

The position-time (x - t) graph for positive acceleration is

The ratio of the distances travelled by a freely falling body in the 1^st, 2^nd, 3^rd and 4^th second