What is the First Derivative of Kinetic Energy?

  • Thread starter Thread starter Jason03
  • Start date Start date
  • Tags Tags
    Derivative
Click For Summary
SUMMARY

The first derivative of Kinetic Energy (KE), represented by the equation KE = 1/2 mv², results in the expression for power, which is mva. This derivation utilizes the power rule of calculus, where the derivative of v² is 2v(dv/dt), with dv/dt representing acceleration. The mass (m) is treated as a constant in this context, as it does not change with time, clarifying the confusion surrounding the differentiation process.

PREREQUISITES
  • Understanding of Kinetic Energy formula (KE = 1/2 mv²)
  • Familiarity with calculus, specifically the power rule
  • Basic knowledge of derivatives and their applications in physics
  • Concept of acceleration (dv/dt) in relation to velocity
NEXT STEPS
  • Review the power rule in calculus for differentiation
  • Study the relationship between Kinetic Energy and work-energy principles
  • Explore the concept of power in physics and its mathematical representation
  • Investigate how mass affects Kinetic Energy in various physical scenarios
USEFUL FOR

Students preparing for the FE exam, physics enthusiasts, and anyone seeking to deepen their understanding of the relationship between Kinetic Energy, power, and calculus.

Jason03
Messages
161
Reaction score
0
I had a question on the first derivative of Kinetic Energy...This a problem from the FE exam...

Now the solution is = mva...which turns out to be power...im just trying to understand how they came up with that...

so KE = 1/2 mv^2


im asuming they are using the general power rule so v^2 would be 2v dv/dt where dv/dt is acceleration...

the m is where I am confused...the derivative of m would just be 1...but why not dm/dt as well...obviously it wouldn't make sense because the mass wouldn't change with time...but i guess I am rusty on the power rule...
 
Physics news on Phys.org
Jason03 said:
I had a question on the first derivative of Kinetic Energy...This a problem from the FE exam...

Now the solution is = mva...which turns out to be power...im just trying to understand how they came up with that...

so KE = 1/2 mv^2


im asuming they are using the general power rule so v^2 would be 2v dv/dt where dv/dt is acceleration...

the m is where I am confused...the derivative of m would just be 1...but why not dm/dt as well...obviously it wouldn't make sense because the mass wouldn't change with time...but i guess I am rusty on the power rule...


m is a constant, v is the only thing changing with time, that's why you differentiate the v2 with respect to t
 
perfect!...that makes sense...I thought it was something to do with mass not changing...but i forgot i was taking the derivative with respect ot time...

thank you
 

Similar threads

Apostol question about the differential equations of a falling object
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Power done by work on a continuous body isn't the derivative of work?
  • · Replies 11 ·
Replies
11
Views
2K
Variable mass system : water sprayed into a moving container
  • · Replies 27 ·
Replies
27
Views
1K
Derivative of a function of a function - .
  • · Replies 2 ·
Replies
2
Views
1K
Differential equation for air resistance
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Kinetic Energy derivation assumption?
  • · Replies 11 ·
Replies
11
Views
2K
High School How does this derivative work? And why the speed of light remains?
  • · Replies 7 ·
Replies
7
Views
438
Thermal Energy Equation Term - Chain Rule
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Derivation of Hamilton's Principle: Questions
  • · Replies 19 ·
Replies
19
Views
1K
Derivation of the Continuity Equation for Fluids
  • · Replies 6 ·
Replies
6
Views
2K