If $v = x^2 - 5x + 4$,find the acceleration of the particle when the velocity of the particle is zero.

$A$ particle is moving in a straight line such that its velocity is increasing at $5\,m/s$ per meter. The acceleration of the particle is .......... $m/s^2$ at a point where its velocity is $20\,m/s$.

If $v$ is the velocity of a body moving along the $x$-axis,then the acceleration of the body is .........

$A$ 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

Match the following columns.

Column $I$	Column $II$
$(A)$ $\frac{dv}{dt}$	$(p)$ Acceleration
$(B)$ $\frac{d|v|}{dt}$	$(q)$ Magnitude of acceleration
$(C)$ $\frac{dr}{dt}$	$(r)$ Velocity
$(D)$ $\left|\frac{dr}{dt}\right|$	$(s)$ Magnitude of velocity

What is retardation? What is its direction?