A particle moving eastwards with 5 m / s^-1. In 10 s the velocity changes to 5 m / s^-1 north

step 1 In this question we will learn about some basic concept of the vectors. The question is a partic

A particle moving eastwards with 5 m / s^-1. In 10 s the...

A particle moving eastwards with $5 \mathrm{~m} / \mathrm{s}^{-1}$. In $10 \mathrm{~s}$ the velocity changes to $5 \mathrm{~m} / \mathrm{s}^{-1}$ northwards. The average acceleration in this time is (A) $\frac{1}{\sqrt{2}} \mathrm{~m} / \mathrm{s}^{-2}$ towards Northeast (B) $\frac{1}{2} \mathrm{~m} / \mathrm{s}^{-2}$ towards North (C) $\frac{1}{\sqrt{2}} \mathrm{~m} / \mathrm{s}^{-2}$ towards Northwest (D) Zero

A particle moving eastwards with $5 \mathrm{~m} / \mathrm{s}^{-1}$. In $10 \mathrm{~s}$ the velocity changes to $5 \mathrm{~m} / \mathrm{s}^{-1}$ northwards. The average acceleration in this time is
(A) $\frac{1}{\sqrt{2}} \mathrm{~m} / \mathrm{s}^{-2}$ towards Northeast
(B) $\frac{1}{2} \mathrm{~m} / \mathrm{s}^{-2}$ towards North
(C) $\frac{1}{\sqrt{2}} \mathrm{~m} / \mathrm{s}^{-2}$ towards Northwest
(D) Zero

Key Concepts

Magnitude and Direction of a Vector

The magnitude of a vector represents its size or length, while the direction indicates where the vector is pointing. Using the Pythagorean theorem for components helps in computing the magnitude, and trigonometric functions are used to determine the angle of the vector relative to a reference axis.

Component Representation in a Coordinate System

Representing vectors in a coordinate system involves breaking them down into perpendicular components, usually along the x- and y-axes. This allows for easier computation of vector operations such as addition, subtraction, and finding the magnitude and direction of the resultant vector.

Average Acceleration

Average acceleration is defined as the change in velocity divided by the time interval over which the change occurs. It is a vector quantity that gives both the magnitude and direction of the acceleration, and it summarizes the overall effect of forces acting on an object over a specific period.

Velocity as a Vector

Velocity is a vector quantity that includes both a magnitude (speed) and a direction. This means that velocities pointing in different directions, even if they have the same speed, are fundamentally different. Understanding velocity as a vector is crucial when analyzing motion in multiple dimensions.

Vector Subtraction

Vector subtraction is used to determine the change in velocity by subtracting the initial velocity vector from the final velocity vector. This process involves dealing with both the magnitude and direction of the initial and final velocities to find the resultant change.

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