Free help with homework

Why join Brainly?

  • ask questions about your assignment
  • get answers with explanations
  • find similar questions

The velocity of a particle moving in the positive direction of the x axis varies as V =k root s where k is a positive constant. nature of v-t graph

a)parabola. b)hyperbola. c)straight line
give reason



This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
V = k √s
       v is velocity,  k is a positive constant and s is the displacement.
=>  v = ds/dt = k √s
=> ds/√s = k dt
Integrate on both sides, with C as the integration constant.
   =>  2 √s  = k t + C
Let us say that displacement s is 0, at t = 0.  Then, C = 0.
  2 √s = k t
=>  s = (k²/4) * t²

Differentiate wrt t to get velocity time function.
  v = ds/dt = (k²/2) * t

Since velocity is a linear function of t,  the v-t graph is a straight line.
Another way:

v = k √s        or  s = v² / k

differentiate wrt t:    ds/dt = 2 v dv/dt * 1/k
as  ds/dt = v we get,
 =>  dv/dt = k / 2
 =>  v = (k/2)  t  + C

So veloccity time graph is a straight line.

1 5 1
The Brain
  • The Brain
  • Helper
Not sure about the answer?
Learn more with Brainly!
Having trouble with your homework?
Get free help!
  • 80% of questions are answered in under 10 minutes
  • Answers come with explanations, so that you can learn
  • Answer quality is ensured by our experts