The distance travelled by a body moving along a line in time $t$ is proportional to $t^3$. The acceleration-time $(a, t)$ graph for the motion of the body will be

Draw the $x-t$ graphs for positive,negative,and zero acceleration.

$A$ particle has a velocity in the negative direction and a constant acceleration in the positive direction. Match the following columns:

Column $I$	Column $II$
$(A)$ Velocity-time graph	$(p)$ Slope $\rightarrow$ negative
$(B)$ Acceleration-time graph	$(q)$ Slope $\rightarrow$ positive
$(C)$ Displacement-time graph	$(r)$ Slope $\rightarrow$ zero
	$(s)$ $|\text{Slope}| \rightarrow$ increasing
	$(t)$ $|\text{Slope}| \rightarrow$ decreasing
	$(u)$ $|\text{Slope}| \rightarrow$ constant

The motion of a particle along a straight line is described by the function $x = (2t - 3)^2$,where $x$ is in metres and $t$ is in seconds. The acceleration of the particle at $t = 2 \,s$ is (in $\,m/s^2$)

Define acceleration,average acceleration,and instantaneous acceleration.

$A$ point moves in a straight line so that its displacement $x \ m$ at time $t \ s$ is given by $x^2 = 1 + t^2$. Its acceleration in $m/s^2$ at a time $t \ s$ is