If the force acting on a body is inversely proportional it's speed, the kinetic energy of the body isCorrect answer : directlyproportional to timeHow to solve?

Question

Answer

Answer

From , K.E=1/2m v^2....from,v=at.k.E=1/2m(at)^2.k.E=1/2ma^2t^2now, multiply numerator n denominator by m...k.E=1/2m a^2 t^2 ×m/m.(from F=ma)k.E=F^2t^2/2m.now, multiply numerator n denominator by v,K.E=F^2t^2/2m ×v/v.k.E=F^2 t t v/2m v.fom,a=v/tk.E= F^2 t v /2 m a .we know F= ma.k.E= m^2a^2 t v /2 m a.k.E= ma t v /2.k.E= F t v / 2.here, F is inversely proportional to v and kinetic energy is directly proportional to t.

Answer

It is hypothetical question

Answer

Answer

The relationship between force, speed, and kinetic energy

The relationship between force, speed, and kinetic energy can be understood by analyzing the given statement: 'the force acting on a body is inversely proportional to its speed.'

Understanding the concept
When a force acts on an object, it can accelerate or decelerate its motion. If the force acting on a body is inversely proportional to its speed, it means that as the speed of the body increases, the force acting on it decreases, and vice versa.

Explaining the relationship with equations
To understand the relationship between force, speed, and kinetic energy, let's consider the equations related to these concepts:

1. Force (F) = mass (m) x acceleration (a)
2. Speed (v) = distance (d) / time (t)
3. Kinetic energy (KE) = 1/2 x mass (m) x speed^2 (v^2)

Considering the given statement, we can write the equation for force as:
F = k / v

Where k is a constant of proportionality.

Deriving the relationship
To determine the relationship between kinetic energy (KE) and time (t), we need to express speed (v) in terms of time (t).

From the equation for speed (v = d / t), we can rewrite it as:
v = k1 x t

Where k1 is another constant of proportionality.

Substituting this value of speed (v) in the equation for force (F = k / v), we get:
F = k / (k1 x t)

Simplifying further, we have:
F = k2 / t

Where k2 = k / k1

Relationship between force and time
From the above equation, we can observe that force (F) is inversely proportional to time (t). As time increases, the force acting on the body decreases, and vice versa.

Relationship between kinetic energy and time
To determine the relationship between kinetic energy (KE) and time (t), we need to analyze the equation for kinetic energy (KE = 1/2 x m x v^2).

Substituting the value of speed (v = k1 x t) in the equation for kinetic energy, we get:
KE = 1/2 x m x (k1 x t)^2

Simplifying further:
KE = 1/2 x m x k1^2 x t^2

From this equation, it is evident that kinetic energy (KE) is directly proportional to time (t). As time increases, the kinetic energy of the body also increases, and vice versa.

Conclusion
In conclusion, when the force acting on a body is inversely proportional to its speed, the kinetic energy of the body is directly proportional to time. As time increases, the kinetic energy of the body also increases.

Similar Class 11 Doubts

An iron bar of length l cm and cross section A cm2 is pulled by a force F dynes from the ends so as to produce an elongation l cm. Which of the following statements is correct?

The average kinetic energy of a molecule

Viscous force is

the degree of dissociation of N2O4 obeying the equilibrium N2O4=2NO2 is related to pressure by ( = implies gives rise to ) solution:the answer is it is inversely proportional to √p explain how?

the degree of dissociation of N2O4l obeying the equilibrium N2O4=2NO2 is related to pressure by ( = implies gives rise to ) solution:the answer is it is inversely proportional to √p explain how?

Top Courses for Class 11View all

Chemistry Class 11

CUET Mock Test: Humanities Subjects 2025

English Class 11

Mathematics (Maths) Class 11

Psychology Practice Tests: CUET Preparation

Top Courses for Class 11

Top Courses for Class 11

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams