If a body starts from rest and travels $120 \,cm$ in the $6^{th}$ second,what is the acceleration in $m/s^2$?

The velocity of a particle moving along the $x$-axis varies as a function of time $t$ as $v(t) = (1 - 3t^2 + 2t^3) \ m/s$. If its position at $t = 0$ is $x = 0$, then at $t = 2 \ s$, its position is: (in $m$)

Consider a vehicle moving with a velocity $54 \,km/h$. At a distance of $400 \,m$ from the traffic light, brakes are applied. The acceleration of the vehicle after the application of brakes is $-0.3 \,m/s^2$. The vehicle's position relative to the traffic light is: (in $\,m$)

Two cars $A$ and $B$ are initially at rest at the same point. If car $A$ starts with a uniform velocity of $40\, m/s$ and car $B$ starts in the same direction with a constant acceleration of $4\, m/s^2$,then after how much time will car $B$ catch car $A$?

$A$ car moving along a straight highway with a speed of $126 \; km/h$ is brought to a stop within a distance of $200 \; m$. What is the retardation of the car (assumed uniform in $m/s^2$)?

$A$ 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