$A$ train starting from rest first accelerates uniformly up to a speed of $80 \ km/h$ for time $t$,then it moves with a constant speed for time $3t$. The average speed of the train for this duration of journey will be (in $km/h$):

Match the following columns.

Column $I$	Column $II$
$(A)$ Constant positive acceleration	$(p)$ Speed may increase
$(B)$ Constant negative acceleration	$(q)$ Speed may decrease
$(C)$ Constant displacement	$(r)$ Speed is zero
$(D)$ Constant slope of $a-t$ graph	$(s)$ Speed must increase

The relation between time $t$ and distance $x$ is given by $t = \alpha x^2 + \beta x$,where $\alpha$ and $\beta$ are constants. The retardation of the particle is:

$A$ particle moves along the straight line $y=3x+5$. Which coordinate changes at a faster rate?

$A$ point traversed half of the distance with a velocity $v_0$. The remaining part of the distance was covered with velocity $v_1$ for half the time and with velocity $v_2$ for the other half of the time. The mean velocity of the point averaged over the whole time of motion is

In what different ways can the velocity of an object be changed?