Question

8 A car is traveling along a track in the shape of a curve with polar equation $r = 3 + 2 \cos(\theta)$ km. At time $t = 0$ seconds the car is at $\vec{r}(0) = (5, 0)$ km (cartesian coordinates) and $\vec{T}(0) = (0, 1)$. (A) If the car travels at a constant speed of 10 meters per second then how long does it take to complete one trip around the track? (B) Decompose the acceleration into tangential and normal components at 1 minute. (C) What is the curvature of the track at the position where the car is at time 1 minute?

          8 A car is traveling along a track in the shape of a curve with polar equation $r = 3 + 2 \cos(\theta)$ km. At time $t = 0$ seconds the car is at $\vec{r}(0) = (5, 0)$ km (cartesian coordinates) and $\vec{T}(0) = (0, 1)$. (A) If the car travels at a constant speed of 10 meters per second then how long does it take to complete one trip around the track? (B) Decompose the acceleration into tangential and normal components at 1 minute. (C) What is the curvature of the track at the position where the car is at time 1 minute?

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8 A car is traveling along a track in the shape of a curve with polar equation r = 3 + 2 cos(θ) km. At time t = 0 seconds the car is at r⃗(0) = (5, 0) km (cartesian coordinates) and T⃗(0) = (0, 1). (A) If the car travels at a constant speed of 10 meters per second then how long does it take to complete one trip around the track? (B) Decompose the acceleration into tangential and normal components at 1 minute. (C) What is the curvature of the track at the position where the car is at time 1 minute?

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University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Banhishikha Sinha

05/11/2021

Step 1

The polar equation r = 3 + 2cos(θ) can be converted to Cartesian coordinates using the following formulas: x = rcos(θ) y = rsin(θ) Substituting the given equation, we have: x = (3 + 2cos(θ))cos(θ) y = (3 + 2cos(θ))sin(θ) Show more…

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8 A car is traveling along a track in the shape of a curve with polar equation r = 3+2 cos0 km. At time t = 0 seconds the car is at r(0) = (5,0) km (cartesian coordinates) and T(0)=(0,1). (A) If the car travels at a constant speed of 10 meters per second then how long does it take to complete one trip around the track? B) Decompose the acceleration into tangential and normal components at 1 minute C) What is the curvature of the track at the position where the car is at time 1 minute?

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