Explanation Given: (P1) Particle with polar coordinates at time t are r = t , θ = t (P2) Particle with rectangular coordinates at time t are x = t , y = t Formula used: (F1) For a moving particle let the polar coordinates at time t be ( r ( t ) , θ ( t ) ) , then, the particle’s speed is, s = ( d r d t ) 2 + r 2 ( d θ d t ) 2 (F2) For a moving particle let the rectangular coordinates at time t be ( x ( t ) , y ( t ) ) , then, the particle’s speed is, s = ( d x d t ) 2 + ( d y d t ) 2 Calculation: For particle P1, using the formula (F1) we get, s = ( d r d t ) 2 + r 2 ( d θ d t ) 2 = ( d

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Author: Rogawski

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Chapter 12.4, Problem 44E

To determine

Part (a): Speed at time $t = 1$ , for a particle with polar coordinates at time $t$ are $r = t, θ = t$

Part (b): Speed at time $t = 1$ , for a particle with rectangular coordinates at time $t$ are $x = t, y = t$

Part (c): why is the speed increasing in one case and constant in the other

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Chapter 12.4, Problem 43E

Chapter 12.5, Problem 1PQ

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Chapter 12 Solutions

ACHIEVE STANDALONE ACCESS F/ CALC 4E

Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 7PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

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Part (a): Speed at time t = 1 , for a particle with polar coordinates at time t are r = t , θ = t Part (b): Speed at time t = 1 , for a particle with rectangular coordinates at time t are x = t , y = t Part (c): why is the speed increasing in one case and constant in the other

Solution Summary: The author explains that the speed is increasing in one case and constant in the other because of uniform increment in path along both the axes in case of rectangular coordinates.

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Part (a): Speed at time $t = 1$ , for a particle with polar coordinates at time $t$ are $r = t, θ = t$

Part (b): Speed at time $t = 1$ , for a particle with rectangular coordinates at time $t$ are $x = t, y = t$

Part (c): why is the speed increasing in one case and constant in the other

Want to see the full answer?

Chapter 12 Solutions

Part (a): Speed at time t = 1 , for a particle with polar coordinates at time t are r = t , θ = t Part (b): Speed at time t = 1 , for a particle with rectangular coordinates at time t are x = t , y = t Part (c): why is the speed increasing in one case and constant in the other

Solution Summary: The author explains that the speed is increasing in one case and constant in the other because of uniform increment in path along both the axes in case of rectangular coordinates.

Videos

Part (a): Speed at time t=1, for a particle with polar coordinates at time t are r=t,θ=t Part (b): Speed at time t=1, for a particle with rectangular coordinates at time t are x=t,y=t Part (c): why is the speed increasing in one case and constant in the other

Want to see the full answer?

Chapter 12 Solutions

Part (a): Speed at time $t = 1$ , for a particle with polar coordinates at time $t$ are $r = t, θ = t$

Part (b): Speed at time $t = 1$ , for a particle with rectangular coordinates at time $t$ are $x = t, y = t$

Part (c): why is the speed increasing in one case and constant in the other