A community for students.
Here's the question you clicked on:
 0 viewing
marigirl
 one year ago
Need clarification please
Topic: Related rates of change Differentiation
show that:
\[\frac{ d }{ dx }(\frac{ v^2 }{ 2 })=\frac{ d^2x }{ dt^2 }\]
Where x represents the distance travelled in t seconds by a particle moving with velocity v
This is what i have so far:
marigirl
 one year ago
Need clarification please Topic: Related rates of change Differentiation show that: \[\frac{ d }{ dx }(\frac{ v^2 }{ 2 })=\frac{ d^2x }{ dt^2 }\] Where x represents the distance travelled in t seconds by a particle moving with velocity v This is what i have so far:

This Question is Closed

marigirl
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{ dx }{ dt }=v\] Differentiate this with respect to time and get \[\frac{ d^2x }{ dt^2 }=\frac{ dv }{ dt } \]

marigirl
 one year ago
Best ResponseYou've already chosen the best response.1we know: \[\frac{ dv }{ dt }=\frac{ dv }{ dx }\times \frac{ dx }{ dt }\]

marigirl
 one year ago
Best ResponseYou've already chosen the best response.1which is \[\frac{ dv }{ dt }=\frac{ dv }{ dx } \times v\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0By the chain rule, the left hand side is \[\frac{d}{dx}\left[\frac{v^2}{2}\right]=\frac{1}{2}\left(2v\frac{dv}{dx}\right)=v\frac{dv}{dx}\]which you showed is equal to \(\dfrac{dv}{dt}\).

marigirl
 one year ago
Best ResponseYou've already chosen the best response.1I am not sure how you for the left side of the equation you wrote above

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Do you know what the chain rule is?

marigirl
 one year ago
Best ResponseYou've already chosen the best response.1i think the v and t are confusing me because i keep writing x and y. i might try doing it again
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.