At time t=10 s, the velocity of a particle moving in the x-y...

At time $t=10 \mathrm{s}$, the velocity of a particle moving in the $x-y$ plane is $\mathbf{v}=0.1 \mathbf{i}+2 \mathbf{j} \mathrm{m} / \mathrm{s} .$ By time $t=10.1 \mathrm{s},$ its velocity has become $-0.1 \mathbf{i}+1.8 \mathbf{j} \mathrm{m} / \mathrm{s}$. Determine the interval and the angle $\theta$ made by the average acceleration with the positive $x$ -axis.

At time $t=10 \mathrm{s}$, the velocity of a particle moving in the $x-y$ plane is $\mathbf{v}=0.1 \mathbf{i}+2 \mathbf{j} \mathrm{m} / \mathrm{s} .$ By time $t=10.1 \mathrm{s},$ its
velocity has become $-0.1 \mathbf{i}+1.8 \mathbf{j} \mathrm{m} / \mathrm{s}$. Determine the
interval and the angle $\theta$ made by the average acceleration with the positive $x$ -axis.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Average Acceleration

Average acceleration is defined as the change in velocity divided by the time interval over which the change occurs. It provides an overall measure of how quickly the velocity changes, both in magnitude and direction, and is computed by subtracting the initial velocity from the final velocity and then dividing by the elapsed time.

Time Interval

The time interval is the duration over which the change in velocity is measured. It is a key parameter in kinematics for calculating average acceleration, serving as the denominator in the formula that relates change in velocity to acceleration.

Vector Direction Calculation

Determining the direction of a vector, such as the average acceleration, involves calculating the angle it makes with a reference axis (commonly the positive x-axis). This typically involves using trigonometric functions, such as the arctan of the ratio of the vector's y-component to its x-component, to find the angle.

Vector Quantities

In physics, quantities such as velocity and acceleration are vectors, meaning they possess both magnitude and direction. Understanding vectors is crucial for analyzing motion in more than one dimension, as it involves operations like addition, subtraction, and decomposition into components.

Transcript

Please give Ace some feedback