Power is defined as a time-oriented value that computes the rate of doing work. It is defined as the rate at which work is performed on a body. It is directly proportional to the force applied and displacement of the body but changes inversely with respect to time. It can be interpreted as the force exerted on a body to displace it from its initial position. Its formula equals the product of force and displacement divided by the time taken. It is denoted by the symbol P. Its standard unit of measurement is watts (W), and the dimensional formula is given by [M¹L²T^-3].

Displacement with power formula

P = Fd/t

Where,

• P is the power,
• F is the force applied,
• d is the displacement,
• t is the time taken.

Derivation

We have to find the value of displacement, d.

It is known that the power is given by the formula,

P = Fd/t

Dividing both sides by F we get,

P/F = Fd/Ft

P/F = d/t

Multiplying both sides by t we get,

Pt/F = (d/t) t

d = Pt/F

This obtains the formula for displacement with power which says that the displacement of an object is equal to the product of power and time divided by the force applied.

Sample problems

Problem 1: Calculate the displacement if the force of 12 N was applied on an object for 2 s to generate a power of 100 W. 

Solution:

We have,

P = 100

t = 2

F = 12

Using the formula we get,

d = Pt/F

= (100 × 2)/12

= 200/12

= 16.67 m 

Problem 2: Calculate the displacement if the force of 10 N was applied on an object for 3 s to generate a power of 50 W.

Solution:

We have,

P = 50

t = 3

F = 10

Using the formula we get,

d = Pt/F

= (50 × 3)/10

= 150/10

= 15 m 

Problem 3: Calculate the power generated if a force of 20 N is applied on an object for 5 s and displacement is 10 m.

Solution:

We have,

F = 20

t = 5

d = 10

Using the formula we get,

P = Fd/t

= (20) (10)/5

= 200/5

= 40 W

Problem 4: Calculate the power generated if a force of 15 N is applied on an object for 3 s and displacement is 20 m.

Solution:

We have,

F = 15

t = 3

d = 20

Using the formula we get,

P = Fd/t

= (15) (20)/3

= 100 W

Problem 5: Calculate the force applied if a power of 70 W is generated for 11 s and displacement is 7 m.

Solution:

We have,

P = 70

t = 11

d = 7

Using the formula we get,

P = Fd/t

=> F = Pt/d

= 70 (11)/7

= 110 N

Problem 6: Calculate the force applied if a power of 120 W is generated for 20 s and displacement is 5 m.

Solution:

We have,

P = 120

t = 20

d = 5

Using the formula we get,

P = Fd/t

=> F = Pt/d

= 120 (20)/5

= 480 N

Problem 7: Calculate the time taken if a force of 34 N is applied to generate a power of 90 W and displacement is 9 m.

Solution:

We have,

P = 90

F = 34

d = 9

Using the formula we get,

P = Fd/t

=> t = Fd/P

= 90 (34)/9

= 340 s