Explanation Given: Equation of the curve in vector form is r ( t ) = 〈 t 2 , 2 t − t 2 , t 〉 , t = 2 . Formula used: Velocity, v ( t ) = r ' ( t ) Acceleration, a ( t ) = r ' ' ( t ) Tangent vector, T = v ∥ v ∥ Normal vector, N = a N N a N , where a N = ∥ a N N ∥ , a N N = a − a T T and a T = a . T Calculation: We have v ( t ) = r ' ( t ) = 〈 2 t , 2 − 2 t , 1 〉 and a ( t ) = r ' ' ( t ) = 〈 2 , − 2 , 0 〉 At t = 2 , v ( 2 ) = 〈 4 , − 2 , 1 〉 and a ( 2 ) = 〈 2 , − 2 , 0 〉 We know, T = v ∥ v ∥ T = v ∥ v ∥ = 〈 4 , − 2 , 1 〉 21 = 1 21 〈 4 , − 2 , 1 〉 a T = a ...

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Author: Rogawski

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Chapter 14, Problem 34CRE

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The acceleration vector a at the point indicated as a sum of tangential and normal components for $r (t) = 〈 t^{2}, 2 t - t^{2}, t 〉, t = 2$ .

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Chapter 14, Problem 33CRE

Chapter 14, Problem 35CRE

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Chapter 14 Solutions

CALCULUS W/SAPLING ACCESS >IC<

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 6PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E

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The acceleration vector a at the point indicated as a sum of tangential and normal components for r ( t ) = 〈 t 2 , 2 t − t 2 , t 〉 , t = 2 .

Solution Summary: The author explains the equation of the curve in vector form is r (t ) = t 2.

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The acceleration vector a at the point indicated as a sum of tangential and normal components for $r (t) = 〈 t^{2}, 2 t - t^{2}, t 〉, t = 2$ .

Want to see the full answer?

Chapter 14 Solutions

The acceleration vector a at the point indicated as a sum of tangential and normal components for r ( t ) = 〈 t 2 , 2 t − t 2 , t 〉 , t = 2 .

Solution Summary: The author explains the equation of the curve in vector form is r (t ) = t 2.

Videos

The acceleration vector a at the point indicated as a sum of tangential and normal components for r(t)=〈t2,2t−t2,t〉,t=2.

Want to see the full answer?

Chapter 14 Solutions

The acceleration vector a at the point indicated as a sum of tangential and normal components for $r (t) = 〈 t^{2}, 2 t - t^{2}, t 〉, t = 2$ .