$A$ particle moves a distance $x$ in time $t$ according to the equation $x = (t + 5)^{-1}$. The acceleration of the particle is proportional to:

An alpha particle enters a hollow tube of $4 \, m$ length with an initial speed of $1 \, km/s$. It is accelerated in the tube and comes out of it with a speed of $9 \, km/s$. The time for which it remains inside the tube is

An object is moving with a uniform acceleration which is parallel to its instantaneous direction of motion. The displacement $(s)-$ velocity $(v)$ graph of this object is

$A$ car,starting from rest,accelerates at the rate $\alpha$ through a distance $d$,then continues at a constant speed for time $t$ and then decelerates at the rate of $\alpha/2$ to come to rest. If the total distance traveled is $15\, d$,then $d=$

$A$ bus moving along a straight highway with a speed of $72 \,km/h$ is brought to a halt within $4 \,s$ after applying the brakes. The distance travelled by the bus during this time (assume the retardation is uniform) is . . . . . . $m$.

$A$ body of mass $10 \,kg$ has a constant velocity of $10 \,m \,s^{-1}$. $A$ constant force is applied for a duration of $4 \,s$ on the object, which gives it a speed of $2 \,m \,s^{-1}$ in the opposite direction. Find the acceleration produced in it.