$A$ body is moving with a uniform acceleration covers $40\,m$ in the first $4\,s$ and $120\,m$ in next $4\,s.$ Its initial velocity and acceleration are

The distance $x$ covered in time $t$ by a body having initial velocity $u$ and having constant acceleration $a$ is given by $x=ut+\frac{1}{2}at^2$. This result follows from

Consider that a truck is moving initially with $54 \,km/h$. It is stopped by the driver after looking at an obstacle with a deceleration of $10 \,m/s^2$. The distance travelled by the truck before coming to rest is (in $\,m$)

The initial velocity of the particle is $10 \ m/s$ and its retardation is $2 \ m/s^2$. The distance moved by the particle in the $5^{th}$ second of its motion is .......... $m$.

If a body starts from rest and travels $120 \, cm$ in the $6^{th}$ second,then the acceleration of the body is:

$A$ particle is moving along the $X$-axis with velocity $v = e^{-\beta x}$. At time $t = 0$,the particle is located at $x = 0$. The displacement of the particle as a function of time is