The acceleration-time graph is

The area enclosed between a-t curve gives change in velocity for the corresponding interval. At t = 0, v = 0, hence final velocity at t = 3 s will increase to 6 m/s.In next 3 s, the velocity will decrease to zero.
Thus, the velocity-time graph is
  

The horizontal range of the projectile is given by 
R = \(\frac { { u }^{ 2 }sin2\theta }{ g } \)
If angle of projection 
\(\theta ={ 45 }^{ o }-\alpha \quad R={ R }_{ 2 }\)
\({ R }_{ 2 }=\frac { { u }^{ 2 }sin2({ 45 }^{ o }-\alpha ) }{ g } =\frac { { u }^{ 2 } }{ g } cos2\alpha \) 

Hatrick knew that the bullet falls under gravity, when fired. It follows a parabolic path. Peterson was firing the bullet by keeping the gun in the line of the sight and hence missing the target. Thus, the bullet has to be fired by keeping the gun tilted above the line of sight to hit the target.

Yes, the flight of a bird is an example of composition of vectors. As the bird flies, it strikes the air with its wings W, W along WO. According to Newton's third law of motion, air strikes the wings in opposite directions with the same force in reaction. The reactions are OA and OB. From law of parallelogram vectors, OC is the resultant of OA and OB. This resultant upwards force OC is responsible for the flight of the bird.

When a person driving a car suddenly applies the brakes, the lower part of the body slower down with the car while upper part of the body continues to move forward due to inertia of motion. If driver is not wearing seat belt, then he falls forward and his head hit against the steering wheel.

When a cat falls to ground from a height, it stretches its body alongwith the tail so that its moment of inertia become high. Since,\(I\omega \) is to remain constant, the value of angular speed \(\omega \) decreases and therefore the cat is able to land on the ground gently.

The change in gravitational potential energy of a body between two given points depends only upon the position of the given points and is independent of the path followed.is due to the fact that the gravitational force is a conservative force and work done by a conservative force depends only on the position of initial and final poits and is independent of path followed.

The air between the two walls of the thermo flask is evacuated. This prevents heat loss due to conduction and convention. The loss of heat due to radiation is minimized by silvering the inside surface of the double wall. As the loss of heat due to the three processes is minimized the tea remains hot for a long time.

A cooking utensil should be of suitable material, which possesses small valve of specific heat (C), large value of thermal conductivity (K) and low coefficient of expansion \((\alpha )\)

Efficiency of a Carnot engine is given by \(\eta =\left( 1-\frac { { T }_{ 2 } }{ { { T }_{ 1 } } } \right) \)
Where, T₂ = temperature of sink
and T₁ = Temperature of sink source
So for \(\eta \)  = 1 or 100% T₂ = 0 K or heat is rejected into a sink at 0 K temperature.