# 139 - TAM 212 Spring 2004 1.134(a Given At a certain...

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TAM 212 Spring, 2004 1.134 Given: At a certain instant, v and a for a point are (respectively) ( 29 s m / ˆ 4 ˆ 3 j i v + = , and ( 29 2 / ˆ 10 s m k a - = (a) Required: Find (at this instant) dt d / v Solution: s dt d = / v ; and since t e v v ˆ v v = , ( 29 0 / ˆ 4 ˆ 3 ˆ 4 ˆ 3 ˆ 10 ˆ 2 = + + - = = s m s t j i j i k e a (c) Required: n e ˆ (at that instant) (I am going to do this before (b), as we showed in class.) Solution: ( 29 n t t n n n n n t t n t a a a a a / ˆ / ˆ ˆ ˆ e a a e e e a a a - = = + = + = From (a), 0 = t a , so 2 / ˆ 10 ˆ s m a t t k e a - = - , and ( 29 = - = n t t n a a / ˆ ˆ e a e ( 29 k k k - = - - ˆ 10 / ˆ 10 (b) Required: ρ ( at that instant) Solution: ( 29 k e a 10 ˆ / 2 = = n n s r (from (c)) ( 29 10 / ˆ 4 ˆ 3 10 / 10 / 2 2 2 j i + = = = s s r r m 5 . 2 10 / 5 2 = = r 1.139 Given: The path of a point is from left to right along the curve shown, ( 29 ( 29 2 2 3 4 8a y x a + = with a constant x component of the velocity

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139 - TAM 212 Spring 2004 1.134(a Given At a certain...

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