Consider a particle moving along a straight line, whose position as a function of time is given by $s(t)=\alpha t^2-\beta t +\gamma$, where $\alpha=1 \mathrm{~ms}^{-2}, \beta=6 \mathrm{~ms}^{-1}$ and $\gamma=5 \mathrm{~m}$. The average speed of the particle, in $\mathrm{ms}^{-1}$ from $t=0$ to $t=6 \mathrm{~s}$ is:

The following plots show variation of velocity $(v)$ with time $(t)$ of a ball thrown vertically upward, and falling back. Which of the following plots is/are correct?

When a ruler falls vertically, 5 different persons catch it with different reaction times. ( $g=9.8 \mathrm{~m} \mathrm{~s}^{-2}$ )

A. Person A has reaction time of 0.20 s .

B. Person $B$ has reaction time of 0.22 s .

C. Person C has reaction time of 0.18 s .

D. Person D has reaction time of 0.19 s .

E. Person E has reaction time of 0.21 s .

What is the correct order of the distance travelled by the ruler for each person?

In some appropriate units, time $(t)$ and position $(x)$ relation of a moving particle is given by $t=x^2+x$. The acceleration of the particle is