A ball is rolled over a level lawn with initial velocity 8ms^-1. due to the friction the velocity decreases and is given by dv/dt=-2. Find the equation of distance travelled?
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First integrate dv/dt =-2
so it becomes v = -2t +C, at t =0, v=8, plug in, find C then that's the equation of velocity.
then integrate velocity equation
so, what the meaning of equation of distance travelled? add the equation we get or what?
it's the equation of distance travel in term of t, like s(t)= ...., and when you integrate velocity equation, you get distance equation
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So, s(t) = -t^2 +8t +C
And I think at time t=0, the distance travel is 0, so 0= 0+0 +C, so C=0
s(t) = -t^2 +8t is distance equation
does this answer your question ?
why we must integrate the velocity equation again?
At first, you're given dv/dt, which is the derivative of velocity, or acceleration. After you integrate it, it becomes velocity equation, which is v(t) = -2t +8. THen you integrate again to get position equation or distance travel.