Unformatted text preview: V 3 i We can now determine the value of C by using the fact that x = f when v = 2 V . Hence, f = 1 3 C D 8 V 3 − V 3 i = 7 3 C V 3 Finally, solving for C yields C = 7 3 V 3 f (b) For this part of the problem, we must use the definition of acceleration, i.e., a = dv dt = ⇒ dv = a dt = C v dt Hence, we can determine the time from dt = 1 C v dv = 3 7 f V 3 v dv Integration shows that τ = 8 τ dt = 3 7 f V 3 8 3 V V v dv = 3 14 f V 3 v 2 e e e e v =3 V v = V = 3 14 f V 3 D 9 V 2 − V 2 i Therefore, the time at which the particle’s velocity is v = 3 V is τ = 3 14 f V 3 D 8 V 2 i = 12 7 f V...
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 '06
 Shiflett
 Derivative, C= dv dt

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