Under the action of a force, a $2 \,kg$ body moves such that its position $x$ as a function of time $t$ is given by $x=\frac{t^2}{3}$, where $x$ is in metres and $t$ in seconds. The workdone by the force in first two seconds is .......... $J$
Given below are two statements:
Statement $I:$ A truck and a car moving with same kinetic energy are brought to rest by applying brakes which provide equal retarding forces. Both come to rest in equal distance.
Statement $II:$ A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero.
In the light of given statements, choose the most appropriate answer from the options given below.
A body of mass $m= 10^{-2}$ $kg$ is moving in a medium and experiences a frictional force $F= -kv^2$. Its initial speed is $v_0= 10$ $ms^{-1}$. If, after $10\; s$, its energy is $\frac{1}{8}$ $mv_0^2$ the value of $k$ will be
A stone with weight $w$ is thrown vertically upward into the air from ground level with initial speed $v_0$. If a constant force $f$ due to air drag acts on the stone throughout its flight. The maximum height attained by the stone is
A block of mass $10\, kg,$ moving in $x$ direction with a constant speed of $10\, m s^{-1}$, is subjected to a retarding force $F= 0.1\,x \,J/m$ during its travel from $x = 20 \,m $ to $30\, m$. Its final $KE$ will be ............... $\mathrm{J}$