Please wait...
Contact Us
Contact
Need assistance? Contact us on below numbers

For Study plan details

10:00 AM to 7:00 PM IST all days.

For Franchisee Enquiry

OR

or

Thanks, You will receive a call shortly.
Customer Support

You are very important to us

For any content/service related issues please contact on this number

9321924448

Mon to Sat - 10 AM to 7 PM

If a=g-kv then what is the velocity of the particle for very long time and initially particle is at rest fir time t=0? Where a is acceleration g, k is constant and v is velocity.

Asked by namitapandey08062000 11th October 2019, 1:26 PM
Answered by Expert
Answer:
acceleration = a = dv/dt = ( g - kv )
 
begin mathsize 14px style fraction numerator d v over denominator d t end fraction space equals space g space minus space k space v
fraction numerator d v over denominator g space minus space k v end fraction space equals space d t space space space space o r space space space fraction numerator negative k space d v over denominator g minus k v end fraction space equals space minus k space d t
B y space i n t e g r a t i n g space b o t h space s i d e s space
integral subscript 0 superscript v fraction numerator negative k space d v apostrophe over denominator g minus k v apostrophe end fraction space equals space minus k space integral subscript 0 superscript t d t
ln open parentheses fraction numerator g space minus space k space v over denominator g end fraction close parentheses space equals space minus k space t
ln open parentheses 1 minus fraction numerator k space v over denominator g end fraction close parentheses space equals space minus space k space t
1 minus space fraction numerator k space v over denominator g end fraction space equals space e to the power of negative k space t end exponent
v space equals space g over k open parentheses 1 space minus space e to the power of negative k space t end exponent close parentheses space space............ left parenthesis 1 right parenthesis end style
 
From eqn.(1), we see that, at t = 0, velocity v = 0
 
after long time, t →∞ , velocity v = g/k
Answered by Expert 11th October 2019, 3:00 PM
Rate this answer
  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10

You have rated this answer 10/10

Tags: velocity
Your answer has been posted successfully!

Chat with us on WhatsApp