Velocity of a particle moving along a straight line is given by $v = t^2 - 3t - 4 \, (m/s)$. Find the velocity at the instant when no net force is applicable on the particle.......$m/s$ (in $.25$)

$A$ woman starts from her home at $9.00\; am$, walks with a speed of $5\; km\; h^{-1}$ on a straight road up to her office $2.5\; km$ away, stays at the office up to $5.00\; pm$, and returns home by an auto with a speed of $25\; km\; h^{-1}$. Choose suitable scales and plot the $x-t$ graph of her motion.

The acceleration-time graph for a body is shown in the graph. Which of the following graphs would probably represent the velocity of the body plotted against time?

Match Column-$I$ with Column-$II$ based on the distance-time $(d-t)$ graphs provided in the image.

$(1)$ Velocity decreases	$(a)$ Linear graph (constant slope)
$(2)$ Velocity increases	$(b)$ Concave up graph (increasing slope)
$(3)$ Velocity is constant	$(c)$ Concave down graph (decreasing slope)

$A$ particle moves along the $x$-axis in such a way that its $x$-coordinate varies with time according to the equation $x = 4 - 2t + t^2$. The velocity of the particle will vary with time as:

$A$ train starting from rest travels the first part of its journey with constant acceleration $a$,the second part with constant velocity $v$,and the third part with constant retardation $a$,finally being brought to rest. The average speed for the whole journey is $\frac{7v}{8}$. The train travels with constant velocity for what fraction of the total time?