$A$ man throws a ball to a height of $12 \ m$,where it reaches with a speed of $12 \ m/s$. If the man throws the ball such that it just reaches this height,what percentage of energy would he have saved?

$A$ car travelling at a speed of $30 \, km/h$ is brought to a halt in $8 \, m$ by applying brakes. If the same car is travelling at $60 \, km/h$,it can be brought to a halt with the same braking force in ............... $m$.

Two bodies of masses $0.1\, kg$ and $0.4\, kg$ move towards each other with the velocities $1\, m/s$ and $0.1\, m/s$ respectively. After collision they stick together. In $10\, s$,the combined mass travels ............ $m$.

Fill in the blanks:
$(a)$ If the momentum of an object is doubled,its kinetic energy becomes ........
$(b)$ For a perfectly inelastic collision,the coefficient of restitution $e$ $=$ .....
$(c)$ An appliance with $1\,kW$ power consumes $1\,kWh$ of energy in ....... time.

State whether the following statements are true or false:
$(a)$ Power is the vector product of force and velocity.
$(b)$ $1\,kg\,m = 9.8\,J$
$(c)$ When a teacher rubs a blackboard with a duster,they do no work.
$(d)$ Kinetic energy can be negative.

Two rectangular blocks $A$ and $B$ of masses $2 \,kg$ and $3 \,kg$ respectively are connected by a spring of spring constant $10.8 \,Nm^{-1}$ and are placed on a frictionless horizontal surface. The block $A$ is given an initial velocity of $0.15 \,ms^{-1}$ in the direction shown in the figure. The maximum compression of the spring during the motion is (in $\,m$)