Find the Scalar Tangential and Normal Components of Acceleration of a Particle

question 61

Multiple Choice

Find the scalar tangential and normal components of acceleration of a particle with position vector $\mathbf { r } ( t ) = e ^ { t } ( \cos 8 t , \sin 8 t , 8 )$

• A) \(a _ { \mathbf { T } } = \sqrt { 65 } e ^ { t }\) , \(a _ { \mathrm { N } } = 8 \sqrt { 65 } e ^ { t }\)
• B) \(a _ { \mathbf { T } } = 8 \sqrt { 65 } e ^ { t }\) , \(a _ { \mathrm { N } } = \sqrt { 65 } e ^ { t }\)
• C) \(a _ { \mathbf { T } } = 65 e ^ { t }\) , \(a _ { \mathrm { N } } ( t ) = 8 e ^ { t }\)
• D) \(a _ { \mathbf { T } } = 8 e ^ { t }\) , \(a _ { \mathrm { N } } = 65 e ^ { t }\)

---

Definitions:

Population Variances

Measures the degree to which each number in a set differs from the mean of the population, calculated as the average of the squared differences from the Mean.

Normal Populations

Populations that exhibit characteristics of normal distribution, where data points tend to cluster around a central mean value.

Degrees Of Freedom

Degrees of freedom represent the number of independent values or quantities which can freely vary in an analysis without violating any constraints imposed on them.

Pooled Variance

A method used to estimate the variance of two or more populations when the mean of each population may differ but the true variance is assumed to be the same.