Starting from the origin at time $\text{t}=0$, with initial velocity $5 \hat{\mathrm{j}} \mathrm{m} {\mathrm{s}}^{-1}$, a particle moves in the $x$ -$y$ plane with a constant acceleration of $\left(10\hat{\mathrm{i}}+4\hat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-2}$. At time $\text{t}$, its coordinates are $\left(20 \mathrm{m}, y \mathrm{m}\right)$. The values of $t$ and $y$ are, respectively:

The speed verses time graph for a particle is shown in the figure. The distance travelled (in $\mathrm{m}$) by the particle during the time interval $\mathrm{t}=0$ to $\mathrm{t}=5$ $\mathrm{s}$ will be __________.

A balloon is moving up in air vertically above a point $A$ on the ground. When it is a height $h_1,$ a girl standing at a distance d (point B) from A (see figure) sees it at an angle $45°$ with respect to the vertical. When the balloon climbs up a further height $h_2$, it is seen at an angle $60°$ with respect to the vertical if the girl moves further by a distance $2.464 \mathrm{d}$ (point C). Then the height ${\mathrm{h}}_2$ is (given $\tan 30°=0.5774$):

The velocity $\left(v\right)$ and time $\left(t\right)$ graph of a body in a straight line motion is shown in the figure. The point $S$ is at $4.333$ seconds. The total distance covered by the body in $6 \mathrm{s}$ is :

A clock has a continuously moving second's hand of $0.1 \mathrm{m}$ length. The average acceleration of the tip of the hand (in units of $\mathrm{m} {\mathrm{s}}^{-2}$) is of the order of :