A particle is moving eastwards with velocity of 5 m / s. In 10 sec the velocity changes to 5 m

step 1 Our question is a particle going towards eastwards with velocity 5 meter per second in 10 second

A particle is moving eastwards with velocity of 5 m / s. In...

A particle is moving eastwards with velocity of $5 \mathrm{~m} / \mathrm{s}$. In $10 \mathrm{sec}$ the velocity changes to $5 \mathrm{~m} / \mathrm{s}$ northwards. The average acceleration in this time is (a) Zero (b) $\frac{1}{\sqrt{2}} \mathrm{~m} / \mathrm{s}^{2}$ toward north-west (c) $\frac{1}{\sqrt{2}} \mathrm{~m} / \mathrm{s}^{2}$ toward north-east (d) $\frac{1}{2} \mathrm{~m} / \mathrm{s}^{2}$ toward north-west

A particle is moving eastwards with velocity of $5 \mathrm{~m} / \mathrm{s}$. In $10 \mathrm{sec}$ the velocity changes to $5 \mathrm{~m} / \mathrm{s}$ northwards. The average acceleration in this time is
(a) Zero
(b) $\frac{1}{\sqrt{2}} \mathrm{~m} / \mathrm{s}^{2}$ toward north-west
(c) $\frac{1}{\sqrt{2}} \mathrm{~m} / \mathrm{s}^{2}$ toward north-east
(d) $\frac{1}{2} \mathrm{~m} / \mathrm{s}^{2}$ toward north-west

Key Concepts

Average Acceleration

Average acceleration is defined as the change in velocity divided by the time interval during which the change occurs. It is a vector quantity that takes into account both the magnitude and direction of the velocity change, making it essential in kinematics to measure how quickly and in what direction an object's velocity is altering over time.

Vector Subtraction

Vector subtraction is a method used to determine the change in a vector quantity by subtracting the initial vector from the final vector. In problems involving velocities, displacements, or forces, this process accounts for differences in both magnitude and direction, enabling the correct calculation of resultant vectors.

Component Analysis

Component analysis involves breaking a vector into its orthogonal parts along specified axes, typically in a two-dimensional plane, such as horizontal and vertical components. This method simplifies calculations by allowing each component to be handled independently, which is particularly useful when dealing with vector addition or subtraction in kinematic problems.

Magnitude and Direction Determination

After obtaining the vector components through subtraction, the overall magnitude of the resultant vector can be determined using the Pythagorean theorem, and its direction can be found using trigonometric ratios such as the tangent function. This step is crucial for fully characterizing the resultant vector in terms of both its size and the specific direction in which it points.

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