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Uniformly Accelerated Motion Equations

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Questions and Answers

Which equation relates the final velocity (v), initial velocity (u), acceleration (a), and time (t) for uniformly accelerated motion?

v = u - at

v = u / t - a

v = u * t + a

v = u + at (correct)

What does the variable 'a' represent in the equation v = u + at for uniformly accelerated motion?

Displacement

Initial velocity

Acceleration (correct)

Final velocity

If an object has an initial velocity of 5 m/s and an acceleration of 2 m/s^2, what will be its final velocity after 3 seconds of uniformly accelerated motion?

15 m/s

11 m/s (correct)

9 m/s

7 m/s

What is a vector in the context of machine learning and programming?

A vector is a tuple of one or more values called scalars. In machine learning and programming, vectors are often used to represent data, model parameters, and other entities. For instance, the input (3.14159, 2.71828, 1.618) is a vector of 3 elements, and could be represented as a point in 3-dimensional space. Signup and view all the answers

What is the feature vector in the context of machine learning?

The feature vector is simply one row of input data. In the context of machine learning, it could represent the features or attributes of a dataset, such as a house’s year of construction, number of bedrooms, area (m²), and size of garage (auto capacity) in the housing price prediction example. Signup and view all the answers

Why are vectors commonly used in machine learning?

Vectors are commonly used in machine learning as they provide a convenient way to organize and represent data and model parameters, making it easier to perform mathematical operations and algorithms. Signup and view all the answers

What is the significance of vectorizing the data in machine learning?

Vectorizing the data is one of the very first steps in making a machine learning model. It involves transforming the data into a vector form, which is essential for many machine learning algorithms and processes. Signup and view all the answers

How would a program declare a 1x3 array to hold a vector of 3 elements?

A program would declare a 1x3 array (one-dimensional data structure) to hold a vector of 3 elements, such as the input (3.14159, 2.71828, 1.618) in the example. This array would be used to store the values of the vector. Signup and view all the answers

Study Notes

Uniformly Accelerated Motion

The equation relating final velocity (v), initial velocity (u), acceleration (a), and time (t) for uniformly accelerated motion is: v = u + at
The variable 'a' in the equation v = u + at represents the acceleration of the object

Problem Example

If an object has an initial velocity of 5 m/s and an acceleration of 2 m/s^2, its final velocity after 3 seconds of uniformly accelerated motion is: v = 5 + 2(3) = 11 m/s

Vectors in Machine Learning

A vector in the context of machine learning and programming is a quantity with both magnitude and direction, often represented by an array of numbers
The feature vector in the context of machine learning is a vector of numerical values that describe a particular instance or data point
Vectors are commonly used in machine learning because they can be used to represent complex data in a compact and efficient way, and can be easily manipulated and operated on using mathematical operations
The significance of vectorizing the data in machine learning is that it allows for the application of various machine learning algorithms and enables the model to learn patterns and relationships in the data
In programming, a 1x3 array to hold a vector of 3 elements would be declared as: vector myVector = {x, y, z}; or similar syntax depending on the programming language.

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Description

Test your knowledge of the equations for uniformly accelerated motion, including the relationship between displacement, time, initial velocity, final velocity, and acceleration.