Physics

$x=2t-1$

$v=\frac{dx}{dt}=2 m s^{-1}$

$P=F·v$

$=2*5=10 W$

In the case of pure rolling,

The topmost point will have velocity $2v$ while point $Q$ i.e. the lowest point will have zero velocity. Hence point $P$ moves faster than point $Q$ .

According to given truth table, output is independent on value of $A$

$\therefore$ Output $Y=\overline{B}$

Air resistance resists the motion of an object. In this case, the net acceleration is lesser than 'g' and it shrinks as the speed increases. This makes the object to speed up more slowly. Ultimately, it reaches a constant terminal velocity which is lower for large-area ones and higher for heavy and streamlined ones.

Suppose the position-time graph is a straight line, in this case, the velocity is constant. This means that there is no acceleration.
If the graph is curved, velocity is changing, which means that there is acceleration. If the graph is concave, the slopes will get more positive with time. This means that there is positive acceleration. If the graph is cap-shaped, the slope will become more negative with time. This is known as negative acceleration.

To graph motion in a straight line, you need to visualise the relationship between different kinematic quantities like position, velocity and time. Suppose an object moves with a constant velocity, the position-time graph will be a straight line with constant slope. If the object accelerates, the slope of position-time graph will change with time and result in a curved line.

No. Since kinetic energy is a scalar quantity, it only depends on speed of the body and not the direction. So if the direction of the body is changed but the speed remains unchanged, there won't be any effect on the kinetic energy. However, if changing the direction also changes the speed of the body, then kinetic energy of the body will also change.

If you look closely at the formula of kinetic energy (1/2*m*v^2), the velocity is squared which automatically gives a positive integer. And mass of the body can never be a negative value, which leads to the result being a positive integer.

The 1/2 is a result of mathematical calculation, which occurs when we integrate? vdv in the formula of work done according to Newton's second law of motion. Without this, the final result will turn out to be twice of the actual value.