The distance-time graph of a particle at time $t$ makes an angle of $45^{\circ}$ with the time axis. After one second,it makes an angle of $60^{\circ}$ with the time axis. What is the average acceleration of the particle?

If the velocity of a particle is $(10 + 2t^2) \ m/s$,then the average acceleration of the particle between $2 \ s$ and $5 \ s$ is..........$m/s^2$.

Match the items in Column-$I$ with the items in Column-$II$ correctly.

Column-$I$	Column-$II$
$(1)$ Acceleration is positive	$(a)$ Speed of the particle decreases
$(2)$ Acceleration is negative	$(b)$ Speed of the particle increases
	$(c)$ Speed of the particle keeps changing

Explain the acceleration.

$A$ body starts from the origin and moves along the $x$-axis such that its position at any instant is $x = 4t^2 - 12t$,where $t$ is in seconds and $x$ is in meters. What is the acceleration of the particle in $m/s^2$?

$A$ particle is moving in one dimension (along $x$-axis) under the action of a variable force. Its initial position was $16 \,m$ right of the origin. The variation of its position $(x)$ with time $(t)$ is given as $x = -3t^3 + 18t^2 + 16t$,where $x$ is in $m$ and $t$ is in $s$. The velocity of the particle when its acceleration becomes zero is . . . . . . $m/s$.