Since P=F.v and speed=distance/ time i.e v=s/t so P=F.s/t hence P=4F.2s/t/2=4F.2S.2/t equals to 16F.s/t 16P is the answer

Unit Changes for Length, Time, Force, and Power

To determine the change in the unit of power when the unit of length is doubled, the unit of time is halved, and the unit of force is quadrupled, we need to understand the relationships between these quantities.

1. Relationship between Length and Power
Power is defined as the rate at which work is done or energy is transferred. The formula for power is given by:
Power = Work / Time

Work is defined as the force exerted over a distance. The formula for work is given by:
Work = Force * Distance

Therefore, we can infer that power is directly proportional to both force and distance.

2. Relationship between Time and Power
As stated earlier, power is the rate at which work is done. If the time taken to do the work decreases, the power output increases. Therefore, power is inversely proportional to time.

3. Unit Changes
Given that the unit of length is doubled, the unit of time is halved, and the unit of force is quadrupled, we can determine the change in the unit of power.

Let's assume the original units of length, time, force, and power are L, T, F, and P, respectively.

Unit changes:
Length: L -> 2L (doubled)
Time: T -> T/2 (halved)
Force: F -> 4F (quadrupled)

Power Formula:
P = F * L / T

Substituting the unit changes:
New Power (P') = (4F) * (2L) / (T/2)
= 8FL / (T/2)
= 16FL / T

Change in the unit of power:
The new power (P') is equal to 16 times the original power (P). Therefore, the unit of power would change by a factor of 16.

Summary:
When the unit of length is doubled, the unit of time is halved, and the unit of force is quadrupled, the unit of power would change by a factor of 16. This is because power is directly proportional to force and distance, and inversely proportional to time. By applying the given unit changes to the power formula, we obtain a new power that is 16 times the original power.