Why do you fall in the forward direction when a moving bus brakes to a stop and fall backwards when it accelerates from rest?

The following is the distance-time table of an object in motion:

Time in seconds	Distance in metres
$0$	$0$
$1$	$1$
$2$	$8$
$3$	$27$
$4$	$64$
$5$	$125$
$6$	$216$
$7$	$343$

$(a)$ What conclusion can you draw about the acceleration? Is it constant, increasing, decreasing, or zero?
$(b)$ What do you infer about the forces acting on the object?

$A$ bullet of mass $10\, g$ travelling horizontally with a velocity of $150\, m/s$ strikes a stationary wooden block and comes to rest in $0.03\, s$. Calculate the distance of penetration of the bullet into the block. Also,calculate the magnitude of the force exerted by the wooden block on the bullet.

An object of mass $1 \,kg$ travelling in a straight line with a velocity of $10\, m\, s^{-1}$ collides with,and sticks to,a stationary wooden block of mass $5\, kg$. Then they both move off together in the same straight line. Calculate the total momentum just before the impact and just after the impact. Also,calculate the velocity of the combined object.

$A$ hockey ball of mass $200 \,g$ travelling at $10 \,m \,s^{-1}$ is struck by a hockey stick so as to return it along its original path with a velocity of $5 \,m \,s^{-1}$. Calculate the magnitude of the change in momentum of the hockey ball due to the force applied by the hockey stick.

$A$ $8000 \,kg$ engine pulls a train of $5$ wagons,each of $2000 \,kg$,along a horizontal track. If the engine exerts a force of $40000 \,N$ and the track offers a friction force of $5000 \,N$,then calculate the net accelerating force (in $N$).