True or False ### Problem Statements for Discussion:a) The speed meter on my car reads a steady 60 mph, it is impossible that I am accelerating.b) The torsion of a smooth plane curve is zero because B is a constant vector.c) Curvature is the magnitude of dT/ds, which describes the rate at which T turns per unit of length along the curve.### Explanation:1. **Steady Speed and Acceleration:** - When the speedometer of a car shows a constant speed of 60 mph, can acceleration be truly absent? - Consider that acceleration can occur not only due to changes in speed but also due to changes in direction (i.e., centripetal acceleration).2. **Torsion of Plane Curves:** - In the context of 3D space, torsion measures how much a curve twists out of the plane. - A smooth plane curve having zero torsion implies that it lies entirely within a single plane, causing vector B (binormal vector) to remain constant.3. **Curvature and Rate of Turning:** - Curvature represents how sharply a curve bends at a given point. - \(\frac{dT}{ds}\) defines how the tangent vector T changes with respect to the arc length \(s\), which is a measure of the curve’s rate of rotation in space.

The acceleration of body is defined as the rate of change of velocity and the direction of the body.…

a) The speed meter on my car reads a steady 60 mph, it is impossible that I am accelerating. b) The torsion of a smooth plane curve is zero because B is a constant vector. c) Curvature is the magnitude of dT/ds, which describes the rate at which T turns per unit of lenoth along the curve

a) The speed meter on my car reads a steady 60 mph, it is impossible that I am accelerating. b) The torsion of a smooth plane curve is zero because B is a constant vector. c) Curvature is the magnitude of dT/ds, which describes the rate at which T turns per unit of lenoth along the curve

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

True or False

### Problem Statements for Discussion:

a) The speed meter on my car reads a steady 60 mph, it is impossible that I am accelerating.

b) The torsion of a smooth plane curve is zero because B is a constant vector.

c) Curvature is the magnitude of dT/ds, which describes the rate at which T turns per unit of length along the curve.

### Explanation:

1. **Steady Speed and Acceleration:**
- When the speedometer of a car shows a constant speed of 60 mph, can acceleration be truly absent?
- Consider that acceleration can occur not only due to changes in speed but also due to changes in direction (i.e., centripetal acceleration).

2. **Torsion of Plane Curves:**
- In the context of 3D space, torsion measures how much a curve twists out of the plane.
- A smooth plane curve having zero torsion implies that it lies entirely within a single plane, causing vector B (binormal vector) to remain constant.

3. **Curvature and Rate of Turning:**
- Curvature represents how sharply a curve bends at a given point.
- \(\frac{dT}{ds}\) defines how the tangent vector T changes with respect to the arc length \(s\), which is a measure of the curve’s rate of rotation in space.

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