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Question Number 32585 by rahul 19 last updated on 28/Mar/18

A b o d y u n d e r g o i n g S H M a b o u t t h e

o r i g i n h a s i t s e q u a t i o n x = 0 . 2 \cos 5 π t .

F i n d i t s a v e r a g e s p e e d f r o m t = 0 t o

t = 0.7 s e c .

Commented by rahul 19 last updated on 28/Mar/18

Commented by rahul 19 last updated on 28/Mar/18

p l s e x p l a i n t h i s :

t = \frac{n T}{4} + t_{0} \dots \dots \dots .

Answered by Joel578 last updated on 28/Mar/18

x (t) = 0.2 \cos (5 π t)

x (0) = 0.2 \cos (0) = 0.2

x (0.7) = 0.2 \cos (\frac{7}{2} π) = 0

\bar{v} = \frac{Δ x}{Δ t} = \frac{0.2}{0.7} = \frac{2}{7} {ms}^{- 1}

Commented by rahul 19 last updated on 28/Mar/18

a n s . g i v e n i s 2 m / s .

Answered by tanmay.chaudhury50@gmail.com last updated on 20/May/18

a v e r a g e s p e e d = \frac{x_{2} - x_{1}}{t_{2} - t_{1}}

= \frac{0.2 c o s (5 Π \times 0.7) - 0.2 c o s (5 Π \times 0)}{0.7 - 0.0}

= {0.2 c o s (\frac{5 \times 22 \times 0.7}{7}) - 0.2} / 0.7

= \frac{0.2 (c o s 11) - 0.2}{0.7}

= \frac{2}{7} \times {(c o s 11) - 1}

= \frac{2}{7} \times (0.0044256 - 1)

= - 0.2844

p l s c h e c k

Commented by tanmay.chaudhury50@gmail.com last updated on 20/May/18

Answered by ajfour last updated on 20/May/18

T i m e p e r i o d = \frac{2 π}{5 π} = 0.4 s

D i s t a n c e t r a v e l e d i n 0.7 s (= \frac{7 T}{4})

i s = 7 A = 7 \times 0.2 = 1.4 u n i t s

A v e r a g e s p e e d f o r t h i s

d u r a t i o n = \frac{1.4 u n i t s}{0.7 s} = 2 u n i t s / s .

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